Lesson 9 Solving Problems Using Ratios, Rates, Proportions, and Percents

Ratio vs Proportions A ratio is used to compare two quantities. They are sometimes used to compare parts to parts. For example, the ratio of boys to girls is 7 to 3. (7:3 or 7/3) When two ratios are set equal to one another, they create a proportion. You can also use proportions to solve geometry problems, like when we solve similar figures or scale drawings. For example, 7/10 =14/20

Ratio and Proportion Practice A bag contains only red and blue marbles. The ratio of blue marbles to red marbles in the bag is 2 to 3. If there are a total of 15 marbles in the bag, how many marbles in the bad are red. –If the ratio is 2 to 3, how many marbles are in the bag? –What is the next step to figure out how many total marbles in the bag?

Rate A rate is a ratio that compares two different kinds of units. For example, 20 miles per hour is a rate that compares miles to hours.

Like this… Hector paid $31.41 for 4.5 pounds of chicken salad at a deli. At that rate, how much would it cost to buy 2 pounds of chicken salad? –We are going to use a ratio, proportion and a rate. What do you think we need to do to figure out how much he spent on 2 pounds? –How should we write our answer?

Percents A percent is a ratio of a number to 100. For example, 25% can be written as the ratio 25/100. You can use proportions to solve percent problems, but we are going to practice using equations also.

Finding a percent Elmo bought a CD that cost $ He also paid $1.19 in sales tax. What is the percent of the sales tax? –Strategy 1- Set up a ratio of sales tax to total 1.19/17.0. Then we can set up a proportion to find the percent. Remember a percent is a number out of 100. –Strategy 2- We can set up an equation to solve: (part/whole) x 100.

Lets try another A company that makes batteries check 5,000 batteries it recently produced. It found that 25 of the batteries were defective. What percent of the total batteries checked were defective. –Use both strategies. You will get the same answer.

More percents! Sometimes, we need to use a percent to find a part of something. –A computer costs $1,450. Sales tax is 6%. How much will he pay in sales tax? Strategy 1- set up a proportion: %/100 = part/whole. Strategy 2- write an equation. We have the percent and whole. Percent x Whole = Part –Enrich yourself: How much would the computer cost? You can: Add the part to the whole to get the answer Since percents are out of 100, 100% of the price is $1,450. We are adding 6% sales tax. So =106%. Take it from there.

One more type of problem Shelly bought 6 cans of sauce. This is 40% of what is on the shelf. How many cans were on the shelf? –Strategy 1- Set up the proportion: %/100 = is/of or 40/100= 6/x –Strategy 2- Change the percent to a decimal. Divide the whole by the decimal. That is you answer.

Lets practice what we learned! A team won 2 out of 5 games it played last season. If the team played a total of 35 games last season, how many games were won? Kaz can run 5 kilometers in 30 minutes. At that rate, how far could Kaz run in 12 minutes? Mr. Beyda ordered 200 new books for the school library. If 15 of the books he ordered are biographies, what percent of the books ordered are biographies?

Some more The ratio of boys to girls in the school chorus is 6 to 8. If there are a total of 49 students in the chorus, how many boys are in the chorus? The owner of a clothing store is selling a jacket for 175% of it wholesale price. If the wholesale price of a jacket is $25, how much will the clothing store sell it for? If Sarah pays only $45 of her $5,000 credit card bill, what percentage of the bill will she pay?

You know the drill… A computer system that regularly sells for $1,200 is on sale for 25% off. Tristan buys the computer system on sale and pays $58.50 in sales tax. –What was the percent of sales tax? –Show each step of the work you did to solve this problem.