Section 2.6 Percent, Rate, and Mixture Problems 153 What is known? 35% of the monthly income should be spent on housing. The amount spent on housing is $1400. 35% of monthly income is amount spent on housing 0.35x =1400 Express the relationship. 0.35x 1400 = 0.35 0.35 Divide each side by 0.35. x = 4000 Simplify. So, the monthly income of this family is $4000. 1b. An electronics store has a sale price of $1559.99 on a 50-in. plasma HDTV. This price is 40% off the original selling price. What is the original selling price of the television? Solution 1b. What is unknown? The original selling price of the TV is unknown. Let x = the original selling price of the TV. What is known? The sale price is $1599.99. The sale price is 40% off the original selling price. To write the equation, we use the following relationship. Sale price = original price - discount amount 1559.99 = x - 0.40x 1559.99 = 1x - 0.40x 1559.99 = 0.60x 1559.99 0.60 = 0.60x 0.60 Express the relationship. The discount amount is 0.40x. Write x as 1x. Combine like terms: 1x - 0.40x = (1 - 0.40)x = 0.60x Divide each side by 0.60. 2599.98 = x Simplify. So, the original selling price of the plasma HDTV was $2599.98. 1c. Nanette receives a 5% raise at work. She now makes $26,250 per year. What was her annual salary before the raise? Solution 1c. What is unknown? The salary before the raise is unknown. Let x = Nanette’s original salary. What is known? She received a 5% raise. So, her raise is 0.05x. This problem is similar to the markup illustration. So, we use the following relationship to write the equation. Original salary + raise = new salary x + 0.05x = 26,250 1x + 0.05x = 26,250 1.05x = 26,250 1.05x 1.05 = 26,250 1.05 Express the relationship. Write x as 1x. Combine like terms. Divide each side by 1.05. x = 25,000 Simplify. So, Nanette’s salary before her raise was $25,000.
hendricks_beginning_algebra_1e_ch1_3
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