16 If Rodney spins the spinner 32 times, how many times should he get silver? ( 2 Points)

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1 ACL_Quiz 0: CPM_Chapter _End_ *. Rodney and his friend Tom designed a spinner for a game, but Tom didn t come back from winter break, and now Rodney needs to make the spinner so he can turn it in. All that Rodney can remember is the spinner had four colors on it red, blue, black and silver. He also remembers the following: a) The probability of getting red or blue was 8. b) The probability of getting just red was. c) The probability of getting blue or black is If Rodney spins the spinner times, how many times should he get silver? ( Points). Simplify + ( ) 7. The Hitzle s gummy bear factory produces 9,000,000 individual gummy bears each month in it s Chicago factory. The manager of the factory wanted to check up on his product and found that ⅜ of the gummy bears had a strange fishy taste, and ½ of the fishy gummy bears were discolored a grey color. How many gummy bears are gray in color and taste fishy?. Albert bought ½ boxes of citrus fruit, and was told that each box had fruits in them. He knew that he had both oranges and lemons in the boxes, so he grabbed out at random, and found that of them were oranges. If this sample accurately represents what is in all the boxes, how many lemons does Albert have? *. Gabby had a 9 ounce bar of silver, and wanted to find out how much it was worth and saw one selling online for $. ( Points) a) What is the unit rate or price of silver per ounce? b) What is a formula that could be used to figure out the cost (c) of any number of ounces (o) of silver? c) How many ounces of silver would you need to have to have $ worth of silver?. Simplify ( 7 + ( ))- (-) 7. Evaluate (- - x ) when x = - 8. Hank looked in his supply cabinet and found two left over bags of clay. One of the bags weighed lbs, and the other weighed 7 lbs. If Hank wanted to divide the remaining clay into half pound pieces 8 for his next project, how many pieces could he make out of the two bags? *9. Jason is buying two blue-ray trilogy super packs from Amazon. He wants to buy Star Wars, which retails for $0, and Lord of the Rings for $80. Jason has a coupon he can use to purchase one item at % off. Determine how Jason should use his coupon to save the most money, and calculate the total cost he will pay (before tax) for the two trilogy super packs.

2 ACL_7_ Quiz 0 Answers-- You can copy this by hand and use this during a test!!!. First, convert all of the fractions to the same denominator: red + blue = 8 () = 0 red = () = blue + black = 8 () = Since my denominator is ths, I will create a box to represent all of the outcomes, or outcomes. red red red red We know that red is out of (see above) red red red red blue blue blue blue blue blue We know that red and blue together are 0 out of. Add blues to the red, so together they make 0. red red red red blue blue blue blue blue blue black black black black black We know that blue and black together are out of. Add blacks to the blue so together they make Since there is out of that is not labeled, this must be the box for silver. (P) of silver is therefore. Rodney is going to spin the spinner times. We can use a proportion to figure out how many times he should get silver: silver = = x total spins. You should be able to see that x =. Rodney should get silver twice ( ) Multiply the first two mixed numbers, but note one is positive, the other negative + ( ) Change the mixed numbers to improper fractions. + ( ) You will now be adding two negative rational numbers - as a mixed number is 0. First, draw a rectangle that will represent all of the 9,000,000 gummy bears: The problem says that /8 of the gummy bears had a fishy taste, so divide up the rectangle into 8ths, and shade in the /8: This section is /8 that smell fishy This section is /8 that do not smell fishy

3 . cont d The problem then says that ½ of the fishy gummy bears were also grey. Cut the box in half to show this, and shade half of the fishy gummy bears. fishy/discolored fishy/ discolored fishy/discolored / are fishy, but normal in color All of these down here are still not fishy and normal in color The question requests we find the number of gummy bears that are fishy and discolored out of the total. We set up the following expression: fraction fishy/discolored whole x 9,000,000 9,000,000 =, 87, 00. Begin by figuring out how many pieces of fruit Albert would have: The problem says that he has ½ boxes, and that each one has pieces of fruit in it: You could go right to the expression, and evaluate it or draw a picture = = 70 = pieces of fruit Either way you know that there are pieces of fruit. Next, Albert pulled out at random, and found that of them, were oranges. This would also mean that the other 9 fruits must be lemon. This is what the sample looks like: orange lemon lemon orange lemon lemon orange lemon lemon lemon lemon lemon or 9 or of the fruit is oranges. of the fruit is lemons. The question wants to know how many lemons Albert has, which means of = = 0 = lemons

4 . If we were to put the information on an input-output chart, it would look something like this: Weight in oz (x) Total Price (y) 9 With just one set of data points you can figure out the unit rate: output input = 9 (9 9 ) = a) This ratio shows that it costs $ for ounce You can use the unit rate in a formula. To figure out how much the silver costs (c), you would figure out how many ounces (o) you have, and then multiply by $. As a formula, that looks like this: b) (o)=(c) You could use this formula to figure out how many ounces it would take to reach a certain price. So in part c, it gives us the value $, which is the cost (c). We substitute that into the equation we came up with in part b: ( (o)= original equation ) (o) = ( ) multiplicative inverse (o) = c) ounces would cost $ Another way to do part c would be to use a proportion using the original two data points 9 oz & $: dollars = = ; x = ounces 9 x. Simplify ( 7 + ( ))- (-) ( 7 + ( ))- take care of square first ( 7 + ( ))- ( 0)- evaluate the expression in parenthesis ( 0) multiply - with add up remaining integers Answer: 7. Evaluate (- - x ) when x = (- - (-) ) plug the variable in, always use parenthesis to do this (- - ) take care of the square first!! (- - ) (- - ) evaluate the expression inside absolute value (- - ) (- - ) -8 is 8 away from zero; absolute value is always positive (- - ) (-9) evaluate the expression inside parenthesis (-9) multiply - and add remaining integers Answer: 8

5 8. So Hank has two pieces of clay weighing lbs, and another weighing 7 lbs. We want to find out how much 8 all of it weighs together, so we ll add them: + 7 = 8 () + 7 = + 7 = 9 = change ths to 8ths add fractions and whole numbers total clay Hank has The next thing to do is to divide this total amount of clay into pieces weighing of a pound 0 8 = 8 8 = 8 8 = 8 = 0 8 this is a division problem mixed number is made improper flip /reciprocal of fraction on right multiply make mixed For this problem we need to interpret this answer. Hank wants complete pieces, so although he will have a little left over, he can only make 0 pieces weighing ½ lb. out of the clay he has. 9. There are two parts to this question. The first part says that we need to determine how Jason should use his % off coupon. He can either use it on the Lord of the Rings, or he can use it on Star Wars. Since the coupon says he does not pay for % of the item, it means he must pay of 7% of the item, so begin by figuring that out first: 7% of Lord of the Rings 7% of Star Wars 80 = $0 or.7 x 80 = $0 (pay $0 and save $0) 0 = $ or.7 x 0 = $ (pay $ and save $) The quickest way to the answer is to look at it this way: 0 (Star Wars) + 80 (Lord of the Rings) =$0 is what you pay without coupons. As you can see above your choice is to subtract $0 off the total by using the coupon on Lord of the Rings, or Star Wars, and subtract $. 0 (Star Wars) + 80 (Lord of the Rings) =$0-0 (% off LoTR)= $0 or 0 (Star Wars) + 80 (Lord of the Rings) =$0 - (% off Star Wars)= $ Answer: Clearly it would be best to use the coupon on Lord of the Rings, and pay $0 rather than $

6 Quiz 0 Part : Algebra-Solving Equations Solve all of the equations below. In your work make sure you show how you used all of the properties we learned in class, and label your work with the property you used. The properties we have been working with the last two weeks are: additive inverse property, multiplicative inverse property, distributive property and commutative property. I am not as interested in the value of the variable as I am the work you did to get it, thus failure to show your work correctly will result in a significant point loss! ) 8x + x + = 0 ) n + = 7 ) 9 x = ) = (x 7) ) 7 = x ) (x + ) = 7 7) The school s movie club spent $ for the purchase of the complete Lord of the Rings trilogy, Star Wars trilogy, and four Pirates of the Caribbean movies. The Pirates of the Caribbean movies were ½ the price of the Lord of the Rings movies, and the Star Wars movies were $ less than the Lord of the Rings. How much was each movie? ( Points)

7 Answers: ) 8x + x + = 0 ) n + = 7 ) 9 x = 8x - x + + = 0 comm. prop n + = x = - 9 add inv x + 8 = 0 n + - = add inv -x = x = 0-8 add. inv n= -9 ( ) x = ( ) mult inv x = ( ) n = 9 ( 8 ) mult inv. x = ( ) x = ( ) mult inv n= x = 7 ) = (x 7) ) 7 = x ) (x + ) = 7 ( ) = (x 7) () mult inv. -7 = x comm prop -x - = 7 distri. prop -= x -7-7 = x -x - + = 7 + add inv = x add inv = x add inv -x = = x -9 = - x ( ) x = ( ) mult inv ( ) ( 9) = ( x) ( ) mult inv x = = x 7) The school s movie club spent $ for the purchase of the complete Lord of the Rings trilogy, Star Wars trilogy, and four Pirates of the Caribbean movies. The Pirates of the Caribbean movies were ½ the price of the Lord of the Rings movies, and the Star Wars movies were $ less than the Lord of the Rings. How much was each movie? ( Points) Let s keep track of what we know: a) I know that there are three items: Lord of the Rings (l), Star Wars (s), and Pirates (p). b) I know that these items cost $: (l) + (s) + (p) = c) Pirates of the Caribbean movies were ½ the price of the Lord of the Rings : (p)=½(l) d) Star Wars movies were $ less than the Lord of the Rings : (s)= (l) - There are three equations, but with substitution we can make one that we can solve: (l) + (s) + (p) = (l) + (s) + (p) = (l) + (l) - + ½(l)= (p)=½(l) (p)=½(l) (s)= (l) - (s)= (l) - Solve first for (l): After finding (l) you find (p): Find (s): (l) + (l) - + ½(s)= (p)=½(l) (s)= (l) - (l) + (l) + ½(l) - = comm. prop (p)=½(8) (s)= 8 - l - = (p)= $9 Pirates was $9 (s) = Star Wars was $ l - + = + add inv. l= Check: ( ) l = ( ) mult inv (l) + (s) + (p) = l = 8 we now know Lord of the Rings (l) cost $ = Right!