# 4.2 Percent Problems Objectives: Find equivalent fractions, decimals, and percents. Solve problems involving percent. Standards Addressed: 2.1.8.D: Apply.

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4.2 Percent Problems Objectives: Find equivalent fractions, decimals, and percents. Solve problems involving percent. Standards Addressed: D: Apply ratio and proportion to mathematical problems A: Represent and use numbers in equivalent forms.

Ex. 1

In percent statement such as 42% of 80 is 33
In percent statement such as 42% of 80 is 33.6, 42 is the percent rate, 80 is known as the base, and 33.6 is the percentage. If you know two of the parts, you can find the third. You can use proportions to solve percent problems.

The Proportion Method

The Equation Method

Ex. 2

Ex. 3 Find each answer by using the proportion method or the equation method.
What percent of 80 is 15? % * 80 = 15 % = 18.75% Find 115% of 200. 1.15 * 200 = 230 45 is 40% of what number? 45 = .40N N = 112.5

Ex. 4a

Ex. 4b. Kyle bought a coat on sale for \$29. 40
Ex. 4b. Kyle bought a coat on sale for \$ This sale price was advertised as 60% of the original price. What was the original price? 100% - 60% = 40% 29.40 = .40w W = \$73.50

Ex. 5a.

Ex. 5b Find the sales tax rate to the nearest tenth of a percent if the total paid for an item priced at \$50.75 was \$54.05. \$ \$50.75 = \$3.30 P = 3.30 50.75 P = 6.5 % sales tax rate

Ex. 6 a. A family is adding additional rooms to their house
Ex. 6 a. A family is adding additional rooms to their house. The house originally had 1500 square feet of floor space. After the additions are completed, the house will have 1800 square feet of floor space. Find the percent of increase in floor space. = 300 P = .20 20% increase in floor space

25% increase in floor space
Ex. 6b. Suppose that the amount of floor space in Ex 6 a. has been increased from 1500 square feet to 1875 square feet. Find the percent of increase. = 375 P = .25 25% increase in floor space

Ex. 4a. The price of a car that originally sold for \$17,000 has been reduced to \$14, Find the percent of decrease in the price of the car. 17000 – = 2550 P .15 15% decrease in the price of the car

Ex. 7b. Suppose that the price of the car in Example 7 has been reduced from \$17,000 to \$13,430. Find the percent of decrease in the price of the car. 17000 – = 3570 P = .21 21% decrease in the price of the car

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