Unit 5 Proportions and Percents

Transcription

1 Unit 5 Proportions and Percents Section 5 Solving Percents using Proportions Percent Proportion A percent is the rate out of 100, we can use a proportion to find the missing value following the rules of proportions. = Finding the percent Once we identify the part and the whole, we can set up the percent portion to find the percent. Example1) What percent of 100 is 30? The whole is what we are finding the percent of. Usually we can find the whole after the key word of. The 30 is the part. = Since it is already out of 100 it is 30%. =30 The answer is 30%. Example 2 ) What Percent of 250 cars is 90 cars? Here we are looking for a percent of the whole. So the whole is 250. = 250 =9000 Cross Multiply. Then Divide. =36 The answer is 36%. American River College 261 Milano

2 Sometimes the part is larger the whole, using the words in the problem can help you decide which number is the whole. Example 3) A store sells an item for $600, What percent is that of $300? The whole is the $300 even thought the $600 is the larger number. Notice we are still using the rule we want to know the percent of the whole. = = =200 Her we reduced to keep the numbers small. Cross multiplying give the answer. So the answer is 200%. It makes sense to get an answer larger than 100% because the part was more than the whole. Finding the part If we are given the percent and asked to find the part we will still set up the problem the same way. We will just use our variable in a different part of the percent equation. Example 4) What is 20% of 200 people? Using the key word of helps us identify 200 as the whole. = 4000=100x Cross Multiply. X=40 Then Divide. The answer is 40 people that is the part we were looking for. American River College 262 Milano

3 Example 5) Tax in a certain state to 7.5%. You are trying to calculate tax on a Television that cost $1325. What is 7.5% of $1325?. = = = Cross Multiply. Then Divide. Since we are talking a money amount that we need to pay we should round our answers to the nearest cent. $99.38 is the Tax. Example 6) If you Pre order a book you can get a discounted price of $24. If you buy it after its release date the price is 125% of that price. What is the price after the release date? = 3000=100 30= 24 is the whole- it was 125% of $24. Cross Multiply. Then Divide. The answer is $30. Finding the whole When it is the whole that we are looking for we will use the variable where the whole is in the equation. Example 7) 50% of what number is 70? = 7000=50 Cross multiply, then divde. 140 = x The number is 140. American River College 263 Milano

4 Example 8) You are out with 5 friends and split a bill 5 ways. You are asked to pay $32. That is 20% of what amount? = $32 is the part you pay of the whole. 3200=20 160= The bill was $160. Example 9) You need to buy books for the next semester. You get reimbursed for the books but not the tax. If tax is 8.5% - That means your bill is 108.5% of the price of just your books. If the total including tax was , what was the total?. =. The total including tax is the part, without tax matches up with the 100% = = The books cost $ You will have to decide which information is given to determine how to set up your proportion equation. Use the words in the problem to decide which values are the whole, the part and the percent. The key word of often comes before the whole. The is often separates the part from the whole and the percent. American River College 264 Milano

5 Exercise 5.5 NAME: Solve each of the following using the Percent Proportion. 1. What is 20% of 15? 2. What is 36% of 200? 3. What is 128% of 30? is what percent of 15? 5. 2 is 15% of what number? 6. 4 is what percent of 20? 7. 10is 20% of what number? is 15% of what number? is 120% of what number? American River College 265 Milano

6 10. If you currently eat 1800 calories in a day and your doctor tells you to reduce the calories you take in by 20% - how many calories is he asking you to cut back? 11. Sacramento normally get inches of rain a year. If it rains 15 inches this year, what percent of normal is that? 12. I saw 23 boats on the river last weekend. They said that was only 20% of normal. How many boats are normally on the river? American River College 266 Milano

7 13. There were 15 tornados in the county last year; there is usually an average of 10. What percent of the average was there? 14. A local fundraiser is held every year. This year only 120 people showed up. That is only 80% the regular attendance in the past. What number of people have shown up in the past? 15. Your apartment manager has told you that your rent is going up 5%. If you currently pay $560, how much more money will you need to pay with the increase? American River College 267 Milano

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