CHAPTER 3. Think & Discuss (p. 137)

Transcription

1 CHAPTER Think & Discuss (p. 7).,. Minutes Minutes inline swimming, s skating, i s 8i 8. Sample answer: If the graph consists of two non-parallel lines, then there is a single solution. If the graph consists of two parallel lines, there is no solution. If the graph of two lines coincide, there are infinitel man solutions.. Sample answer: If two lines share two points in common, the are the same line, and ever point on that line is a solution.. ; ; no. 7 ; ; es. ; ; es s 8i represents Calories burned.. Swim for min; skate for min Stud Guide (p. 8). ; no. ; es. ; es. ; es. > ; no. 7 9 ; es no solution infinitel man solutions 7 one solution 8, ) < 9 9. Practice and Applications (pp. ). ) ) ; ; es. ; ; no. 8 ; 9 8 ; no. 8; ; es. 9; 7 7; es. 8 8; ; es 7. ; 7 ; no 8. 7 ; 7 ; es ; 8; no Lesson.. Guided Practice (p. ). solution Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

2 Chapter continued.., ,.. Sample answer:,. 7. Sample answer:, ( 7, 7 9 7, 7,, ,,. Infinitel man solutions; the two lines coincide.. No solution; the two lines are parallel and have no points in common.. One solution; the two lines intersect in a single point.. E; one solution. F; no solution 7. B; infinitel man solutions 8. D; one solution 9. A; no solution. C; one solution. one solution. one solution, 8 8, 8, (, 8 7 Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

3 Chapter continued. no solution. one solution. a. Sample answer: ; 7 b. Sample answer: ; c. Sample answer: ; You ordered paperbacks and hardcovers.. infinitel man. infinitel man solutions solutions 7,. Hardcover 8 Number of late balloons (, ) 8 Paperback Number of mlar balloons Total number of balloons 7. no solution 8. one solution 8 9. one solution. one solution 7 7,,. infinitel man solutions. no solution 8 7,. Price per late balloon l m.l.m. Late Number of minutes jogged Rate for jogging Total cost of balloons l 7 7 Total number of miles j w.j.w. Number Price per of late mlar balloons balloon (, 7) 7 Mlar + Number of = minutes walked Number + Rate for of minutes walking jogged m Number of mlar balloons 7 late balloons and mlar balloons Total number of minutes Number of minutes walked CONTINUED Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

4 Chapter continued. CONTINUED minutes walking minutes jogging 7. Price of doubledensit disk densit disks densit Number of double- + Price of high- disk Number of highdensit disks Number of K on a high-densit disk d.h Double densit Time walking (minutes) d w = Number of K on a double-densit disk 7d h 8 Number of doubledensit + disks Number of highdensit = disks Number of regular 8. Number of + batteries in a pack regular packs Number of alkaline batteries in a pack Cost of regular pack Number of alkaline packs High densit You can bu high-densit disks and double-densit disk. Number of = alkaline packs Number of + Cost of regular packs alkaline pack = CONTINUED Time jogging (minutes) Total amount to spend (, ) (, ) h Total amount to spend j Total number of K needed Total number of batteries needed 8. CONTINUED r a.r.a packs of alkaline and packs of regular batteries 9. Let f the travel time in hours of the first bus. Let s the travel time in hours of the second bus. f s miles from the airport f s. consistent and dependent. consistent and independent. inconsistent. triangle; 7 7. a..9. b., Regular Charge (dollars) First bus time (hr) r f (, ) (, ) Alkaline Second bus time (hr),,,,, ; Sample answer: I graphed the lines carefull and found the apparent points of their intersections from the graph. It was eas to see that two of the lines had the same -intercept, so that was one point. The other points I checked algebraicall in the equations to make sure the were solutions. Long-Distance Phone Service Total length of calls (min) a s Copright McDougal Littell Inc. Algebra 7 Chapter Worked-out Solution Ke

5 Chapter continued c. Sample answer: It represents a charge of $ for minutes of long-distance service. If ou make more than minutes of long-distance calls most months, then the first compan with a 9 per minute charge is less. If ou call long distance less than minutes most months, then the second, with no monthl service charge, is less epensive.. Store :.8 Cost of a Digital Camera Store : Store has a better deal if the price of the camera is over $. Sale price (dollars) Regular price (dollars) Technolog Activit. (p. )..,.. 7., 8.. Mied Review (p. ) , ,. 8 7, 7.7, no; es 7. no; no 7. es; es 7. no; no , 7.,.,., Lesson. Developing Concepts Activit. (p. 7) Drawing Conclusions. a (8, ) 8 Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

6 Chapter continued b. c. d. e. f. 8 (, ) (, ) 9. The sum of the equations is a line whose graph contains the point of intersection.. Sample answer: The sum of the two equations is A D B E C F. Since p, q is a solution of the sstem of equations, Ap Bq C and Dp Eq F. At the point p, q, the left-hand side of the sum equation is A D)p B E q Ap Dp Bq Eq C F. So the point p, q is a solution of the sum equation as well.. Guided Practice (p. ) (, 9) 7 (, ) Sample answer: Because the revised equation is alread solved for the other variable, it is the most direct wa to find the value.. There is no solution if ou come up with an equation that is never true, like. There are infinitel man solutions if ou come up with an equation that is alwas true, like.. 8. ( 9,. 7 7, , 7. s.d s d d.d d.d s s d d 7. single-scoop and double-scoop cones ,,, substitution Copright McDougal Littell Inc. Algebra 9 Chapter Worked-out Solution Ke

7 Chapter continued. Practice and Applications (pp. ) ,., no solution., ,, , infinitel man solutions , , or.,. 8., , , 8, ,, infinitel man solutions Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

8 Chapter continued ,, infinitel man solutions. 8, , 8, 8 no solution, or , 7.78 infinitel man solutions ), 7 8 7, , , no solution 7 Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

9 Chapter continued , ,. a. Sample answer: The second equation is equal to times the first, so there are infinitel man solutions.., , b. Sample answer: The left-hand side of the second equation is equal to times the left-hand side of the first equation, but 8, so there are no solutions.. eq. 7 7 eq , ,., 7 7 eq. no solution infinitel man solutions eq., Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

10 Chapter continued , ) b b $ boes; $ b b C H.7 C 8H.97 C 8H 9. C H 88.9 H. H.8 u C.8.7 C.7.8 C. C. u eq. eq. Sample answer: Let the cost per foot of cable and cost per connector. Then. and.. Subtracting the second equation from the first, find.7. Then a -ft cable with connectors will cost 7 $. 8 8s w s w 8 8 w w 8 8w w w w s swim: minutes skate: minutes , The smaller bedroom is ft ; the larger one is 8 ft. 9. Men s time for m freestle (sec) Women s time (sec) Olmpic Times for Men s m Freestle m m Years since 98 Olmpic Times for Women s m Freestle w w Years since 98. m..7 w , 7.88 ; about ears after the 98 olmpics, in the ear 88 summer olmpics, the men s and women s times in the meter freestle will both be about 7. seconds. Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

11 Chapter continued. Sample answer: Athletic performance cannot be epected to improve at the same linear rate indefinitel. First of all, there is some limit to what the human bod can accomplish, and eventuall the graph of performance times would tend to become tangent to the horiontal line at this value. Further, a line would have an -intercept, impling some future time at which the race would be won in seconds, which is impossible.. C. B. a. Sample answers: b. Sample answers: r, s, t 8 c. Sample answers:. Mied Review (p. ). or 7. or or or 7. 8 or 7. or 7. r, s, t r, s, t < Qui (pg. ).., 8.. no solution <, 7, 8 < Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

12 Chapter continued.. Lesson. Activit (p. ) 7. infinitel man solutions no solution... infinitel man solutions.. infinitel man solutions 7. 8.,, no solution , ,. 8,. 9 7, 7 9. s n 9 s n n n 9 8 n n 9 s 97 s 7 n n 7 tickets sold to students tickets sold to non-students a. Region b. Region c. Region d. Region. Guided Practice (p. 9) It must satisf ever inequalit in the sstem.. It is not a solution because it does not satisf inequalit ;.. The line should be solid, and the region above the line should be shaded, not the region below.. ; > ; es. ; > ; no. ; > ; no 7. ; 7 > ; es Practice and Applications (pp. 9-). es. no. es.. Height (in.) Age (ears) 8 Sample answer:, Sample answer:, Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

13 Chapter continued Sample answer:, 9.. Sample answer:, Sample answer:,. C. B. F Sample answer:,. E. A. D Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

14 Chapter continued $8.7 to $8. Jerk weight (lb) Discount price ($) 8 7 j s. s j..9 j. Snatch weight (lb) s Regular price ($) 9 s >.; j.; s j >.. 7. p c..9 9 Weight (lb) Inches over 8 in height lbs. Chlorine level (PPM) lbs.. 8;.9 or.7 c p 7. c. c. p ph level p 8. Aquatic (kg) a 7 9t 9a, a t.a.9 t Terrestrial (kg) 9. Sample answer:. A. C. ; 8. ;. 7; ;.a.9; a t solutions of and solutions of and ; 9t 9a,; 7 Copright McDougal Littell Inc. Algebra 7 Chapter Worked-out Solution Ke

15 Chapter continued infinitel man solutions. Mied Review (p. ) positive correlation 7. relativel no correlation 7. negative correlation , , 7 7. no solution , Lesson. Activit (p. ). at O, C ; at P, C ; at R, C ; at S, C 8; at T, C 8; at U, C 8; at V, C ;. R; O. ; ; can't be done. Guided Practice (p. ). Linear programming is the process of optimiing a linear objective function subject to a set of linear inequalities known as constraints.. The value of the objective function is tested at various points of the feasible region to determine where it is a maimum and/or minimum; the sstem of constraints define the feasible region.. If the feasible region is bounded, the maimum and minimum values of the objective function must occur at a verte, so the value of the objective function is checked at each verte..,,,,,,,. minimum C 7 maimum C 7 8. At, : C At, : C At, : C minimum maimum 7, 8 Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

16 Chapter continued 7., : C 9, : C 9 8 minimum, 9 : C 9 7 maimum. At, : C At 7, : C 7 At, : C: maimum minimum 8. s l s l l, : C, : C 9 minimum C s l At, 8 8 Bu 8 large baskets and sell them for a profit of $8.. Large 7 7 Small s., : C, : C 9 maimum. Practice and Applications (pp. -7) 9., : C, : C minimum, : C maimum, ; C., : C 7, : C minimum, : C 8, : C 7 maimum 8, : C 8., : C, : C, : C ) minimum, : C no maimum; feasible region unbounded.., : C, : C, : C 8, : C maimum minimum 9 9, : C 7 minimum, : C 7, : C 7 9, : C 7 7, : C 7 maimum Copright McDougal Littell Inc. Algebra 9 Chapter Worked-out Solution Ke

17 Chapter continued , : C 7., : C, : C 7, : C 7 no minimum or maimum; feasible region is unbounded., : C, : C 9, : C minimum maimum 7 9, : C 9, : C, : C, : C, : C 7, : C 7 8 no minimum; feasible region is unbounded 8. maimum, : C, : C 7, : C. C.O.B.O B gal quarts.o B B O minimum maimum 8, : C, 8 : C 8, 8 : C 8 9, : C 9, : C minimum maimum, : C.. 8, : C.., : C.., : C.. Purchase of tpe A and 9 of tpe B for a total storage capacit of 8 ft. maimum gal of Orangeade and gal of Berr-fruit for a profit of $. C 8 7, : C 8 8, 9 : C maimum 8, : C 8 8 9, : C 8 7 Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

18 Chapter continued. C $t $.s b. C t s 8 vertices t.s, ; C t s, 9 ; C 9 t, ; C s two points, : C $ $., : C $ $. $, : C $ $. maimum Make jars of tomato sauce and jars of salsa for a profit of $.. C.7p.78b p b p b p b p b 8 8, : C , : C , 88 8 : C.7 8 7, 9 : C , 7 : C Eat about.887 cups of pinto beans and no rice for a total cost of $.8.. C 7. C 8 D A 7. a. C vertices, ;, ; maimum maimum, ;, ; 8, ; two points, ;, ; If the objective function has a certain value at two vertices, it has that same value at each point of the edge connecting them. maimum The closer to the point, on the line segment, the closer the maimum value. If an edge is parallel to the objective function, the value of C is constant all along that edge. The value of the objective function at points along an edge is between the values at the vertices at its endpoints.. Mied Review (p. 8) (, ).., ; C, ; C, ; C, ; C, ; C, ; C (, ) (, ) (, ).. (, ) 8 (, ) (, 7) 7 (, ). f. f 7. f 7. f 8. g 9. g 7. g 7 7. g 7 7 (, ) (, ) (, ) (, ) Copright McDougal Littell Inc. Algebra 7 Chapter Worked-out Solution Ke

19 Chapter continued.., : C 8, : C 8. minimum.., : C 9 minimum. 7.., : C 7 7, 7 : C maimum 8. v p v; Pla games of each. Qui (p. 9).... v p p p, : C 8, : C maimum 7 Algebra Chapter Worked-out Solution Ke, 8 : C 8, 8 : C 8, ; C 7, : C 7. C S L S L S L S L maimum minimum vertices, ;, ; 8, ; small boes and large boes Math and Histor (p. 9). ton tanks ton. 7 trucks. C r t 8 r t r t r t r t, : C, : C 7 7, : C 7 8, : C tanks, trucks maimum Copright McDougal Littell Inc.

20 Chapter continued Lesson.. Guided Practice (p. 7). a b c d; the solution of such an equation is a plane in three-dimensional space; to graph it, find the three intercepts and shade the trianglular region ling in one octant.. false. Sample answer: Octants and quadrants are both distinct regions bounded b the aes, and defined b the signs of the -, - and -coordinates.. To graph a linear equation in three variables, find the three intercepts and shade the triangular region ling in one octant... A,, (,, ) B,, C,, D,, f, 7 f, f, 7 f, f, f,. 8. f, f, f, f, f, f, f, 7 f, 7. C.r.9p. C C... C $ (,, 8) (,, ) (,, ) (,, ) (,, ) (,, ) (,, ).. (,, ) (,, ) (,, ) (7,, ) (,, ) (, 7, ) (,, ) (,, ) (,, ).. (,, ) 7 (,, ).. (,, 9) (,, ).. (, 9, ) (,, ) 9 7 (,, ) 8 (, 8, (,, ) (,, 7) Copright McDougal Littell Inc. Algebra 7 Chapter Worked-out Solution Ke

21 Chapter continued. (7,, ) (,, 7) (, 7, ) (,, ) (,, ) (,, ) (,, ) ( 9,, ) (,, ) 7. (,, ) (,, ).. (,, ) (8,, ) 8.. (,, 7) (,, ) (,, ) (,, ) (,, ) (,, ) (,, ) (,, ) (,, ) 8 (9,, ) 7 9 (,, ) (,, ) (,, ) (,, ) (,, ) (, 8, ) (, 7, ) f, f, f, f, f, f, f, 8 f, f, f, f, 9 8 f, 8 f, 8 8 f, f, (,, ) (,, ) (,, ) (,, ) 8 (,, ) 8 (,, ).. f, 7 7 f, 7 f, f, f, f, f, f, 7 Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

22 Chapter continued. 9. Mied Review (p. 7) f, 9 f, 8 8 f, 8. V w h 7. V w h V 7 V V cubic units V cubic units 8. C.g a 9. C.n p Sample answers: a g C $7 $8 Sample answers: n p C $7. 8 $9. C.7t.c. C.9e.s Sample answers: t c C $8 $. S 8l b Sample answers: l b S $7 $7 Sample answers: e s C 8 $9.7 $. $ <. < < < 8 > < < < < < 7 < < 8. a. C b. Sample answers: C $ $ c. Sample answer: 8 of each kind of spot costs $, so ou don t have enough mone. I would spend $9 on off-peak spots and 7 peak ones. This wa our commercial gets 7 airings rather than and ou are $ under budget. Sample eplanation: I found. the least common multiple of. 8 the given intecepts and divided each one into the LCM to find the coefficients of the variables. Copright McDougal Littell Inc..... m 7 m neither m m perpendicular m m parallel m 8 8 m perpendicular Algebra 7 Chapter Worked-out Solution Ke

23 Chapter continued 7..9r.p 8. Lesson. r p bu red oak boards and 8 poplar boards Activit. (p. 7). 8 8 (,, 8) f, 8 f,. f, (,, ) f., (,,.) f,... f, 7. (,, ) (,, ) (,, ) (., 9,.) (8,, ) (,, ) (, 7,.) (,, ). Guided Practice (p. 8). Sample answers: 7. When ou come up with an impossible solution such as, that tells ou that the original sstem of equations is inconsistent. If there are man solutions, ou would obtain an identit, such as.. Two or more of the planes could coincide.. Solve one of the equations for one variable in terms of the other two, and then substitute this epression into each of the other two equations, obtaining a sstem of two equations in two variables no es. 7.. f,.. f,. (,, ) 7 (,, ) 7 (,, ) (,,.) 7. 9 no 8.. f, f,. (.,, ) 8 (,, ) (,, ) (,, ) 7 Equation 8 8 Equation..7.. f,.7.. f, (,,.7) (,, ) (,, ) (,., ) ,, 7 Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

24 Chapter continued Practice and Applications (pp. 8 8) ,, ,,..s.c.b s c b, c b s b b,., b.b c $, s,, s 9 9.s.b.b.s.b.b.b.b b $, She should invest $, in savings, $, in bonds, and $, in CDs. 9,, , 9, ,, ,, Copright McDougal Littell Inc. Algebra 77 Chapter Worked-out Solution Ke

25 Chapter continued infinitel man solutions,, ,, ,,. 8 no solution ,,.,, Algebra Chapter Worked-out Solution Ke 9 no solution 9 Copright McDougal Littell Inc.

26 Chapter continued ,, ,, , 9, ,, ,, 9 Copright McDougal Littell Inc. Algebra 79 Chapter Worked-out Solution Ke

27 Chapter continued infinitel man solutions,, ,, ,, ,, Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

28 Chapter continued ,, ,, n g d.97 n g d 9. n g d.9 n g d.99 n 9 g d.9 g d 8.97 n g d 9. n g d.8 g d.7 8 g..7 d 8.97 d. n A pound of mied nuts costs $., a pound of granola costs $.7, and dried fruit costs $.89 a pound. f s t f s t 8 s f t g d 8. g $.7 d.89 f f t t g d. f t f t n $. s f t 8 f t 8 f f 8 f 8 f 7 7 t t There were 7 first place finishers, second place finishers, and third place finishers. Copright McDougal Littell Inc. Algebra 8 Chapter Worked-out Solution Ke

29 Chapter continued. Chicken chow mein is $ per portion. 7. s l 9. f c c. Sample answer: f c b. c b.7 f c.7 c.. c c c c s c s l c.d.r.o 8.D.R.O..R.R.O..O..R.. R D Democrat: million Republican: million Other parties: million. a b c. a. Sample answer: f c. c c D R O O 8. c c $ s 8 l l $ sofa: $8 love seat: $ chair: $ b. Sample answer: s $8. a. e r g. b. e e g g.e.e.g.g e.e.r.g r e g r lb empire apples; lb golden delicious; lb red delicious c. Sample answer: You need pounds of berries to make berr tarts for a part. Strawberries cost $. per pound, raspberries cost $. per pound and blueberries cost $. per pound. You have $8 to spend, and plan to use as man pounds of strawberries as of blueberries and raspberries combined. s r b s r b.s r b 8 Bu lb of strawberries, of blueberries. w e g e g 7. 7 g.g..g.g. Mied Review (p. 8).e.g.g. g lb of raspberries and. lb < < 9 < < 9 9 < <. w 8 Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

30 Chapter continued. or or (, 9, ) ( 9,, 7) ( 8,, ) < or > (,, ) 8 < < 8 > > < < < < (,, ) (,, ) < < (, 7, ). or 8 Qui (p. 8). < < < < < < 9 9 <. < 8 or >.. 8 (,, ) > > < (,, ).. ( 7,, ).. (,, ) (,, ) (,, ) (,, ) (,, ) (8,, ) (,, ) (,, ) (,, ) (,, ) (,, ) Copright McDougal Littell Inc. Algebra 8 Chapter Worked-out Solution Ke

31 Chapter continued.. (,, ) ( 8,, ) w s p w s p (, 7, ) (,, ) (,, ) (,, ) no solution 9 s s p s p s p s p p p 9.. f, f, f, f, 7 f, 7 8 8,, 8.. f, f, f, 7 7 f, ,, Chapter Review (pp. 8 88).. one solution;,.. one solution;,. 9 7., 7, w w string plaers, winds, and percussionists infinitel man solutions no solution., 8 Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

32 Chapter continued (,, ) (,, ) (,, ) 9 9., (,, ) (,, ) (,, ) , : C, : C ma, : C min, : C 8, : C ma, : C min,,.. 7., : C min, 9 : C 9, : C, 9 : C 9 8 ma, : C min, : C, : C, : C ma (,, ) ,, (,, ) (,, ),, Copright McDougal Littell Inc. Algebra 8 Chapter Worked-out Solution Ke

33 Chapter continued Chapter Test (p. 89).. one solution;,... no solution infinitel man solutions , 7 one solution;, infinitel man solutions. 8, , : C 7 min, 8 : C 7 8, : C 7 ma, : C ma, 7 : C 7 No min feasible region is unbounded... (,, ) (,, ) (,, ) (,, ) (,, ) (,, ) (,, ) (,, ) (,, ) (, 8, ) 7 7, (,, ) (8,, ) (,, ) 9 f, 9 f, 9 f, 8 Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

34 Chapter continued ,, 7 7 7,, d p.d.7p. Bu packs of plain beads and packs of decorative beads. 8 Chapter Standardied Test (p. 9). C 8 9. E. A. C. C. D 7. E Copright McDougal Littell Inc no solution C c u c u 8 c u c u Order chest freeers. This will give a profit of $8 at a cost of $,. 8. A B. B. B. a. b. c. = + (, ), 8 8,. Sample answers: a. b. c. d. In part a, I used a different slope and a point on the given line. In part b, I used the same slope but not the same intercept. Therefore, the lines are parallel. In part c, I used a multiple of the same line. That wa the lines coincide.. a. < b. c. not within recommended levels d. Sample answer: LDL: mg/dl HDL: mg/dl Total: 7 mg/dl = 8 (, ) 8 8, (7, ) (, ) (, ) 8 d. The linear form took the least time. e. Sample answer: One solution is LDL mg/dl, HDL. Then total/hdl.7 <. Algebra 87 Chapter Worked-out Solution Ke

35 Chapter continued Chapter Cumulative Practice (pp. 9 9).,,,,. < or < 8 8 > > 8..9,,.9,,. < < > > ,., 9,,.. inverse propert of multiplication. distributive propert. associative propert of multiplication a.. n n or or. 7 or 7.. r d. h V. h A t r b b. > >. 7. or > or 7 7 < no > es.. > 7 88 Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

36 Chapter continued... infinitel man solutions , ,, 8,, no solution all points in shaded region. 8. m 7 m 9 perpendicular (,, ) (,, ) all points in shaded region. m. m neither (,, ) (,, ) (,, ) (,, ) (,, ) (,, ) f 7 f f f 8 7. R.7 8. R $ 8. $.. f,. f, Copright McDougal Littell Inc. Algebra 89 Chapter Worked-out Solution Ke

37 Chapter continued T d t; speed in mph Material (millions of tons) Sample answer: m 7 t Time (ears).. 8. million tons Cost (dollars) = = Miles 77. mi C.9v.79b v, b v b v b, : C.9.79 $8. pounds of beef and pounds of vegetables will minimie the cost. Total cost: $8. v v = b Vegetables 7 v = b 7 Beef b 9 Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.