Section PF.3 – Percent Increase and Percent Decrease
In the previous section, we calculated the relative, or percent, change. Now, we will use the idea of percent change to determine the future value of the quantity.
| Example 1 |
| In the news, you hear “tuition is expected to increase by 7% next year.” If tuition this year was $1,200.00 per quarter, what will it be next year? |
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There are two ways to approach this problem: 1. The tuition next year will be the current tuition plus an additional 7%, so it will be 100% + 7% = 107% of this year’s tuition. Calculate 107% of $1,200: $1,200(1.07) = $1,284. 2. Alternatively, we could have first calculated 7% of $1,200: $1,200(0.07) = $84.00. Notice this is NOT the expected tuition for next year (we could only wish). Instead, this is the expected increase, so to calculate the expected tuition, we’ll need to add this change to the previous year’s tuition: $1200 + $84 = $1,284.00. |
| Example 2 |
| A TV originally priced at $869.00 is on sale for 35% off. Determine the sale price of the TV. |
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There are a couple of ways to approach this problem: After the discount, you will wind up paying 100% – 35% = 65% of the original price of the item. Calculate 65% of the original price to find the sale price: $869(0.65) = $564.85. Alternatively, we could have first calculated 35% of $869: $869(0.35) = $304.15. Notice this is the amount of the discount, NOT the sale price! So, to calculate the sale price, we will need to subtract discount from the original price of the item: $869 – $304.15 = $564.85. |
| You Try PF.3.A |
| a. The bill for dinner (after tax) was $85.20. You decide to leave a 15% tip. Calculate the total amount paid.
b. A clothing store is having a 15% off sale. Determine the sale price for an item that was originally priced at $74.00. |
| Example 3 |
| You purchased a new phone in Scottsdale, which has 7.95% sales tax. The total cost (including tax) for your new phone was $505.40. What was the pre-tax price? |
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To compute the pre-tax price, we need to understand what the $505.40 represents. Since $505.40 is the total cost including tax, we know: Cost of phone + tax = $505.40 We know the dollar amount of tax is 7.95% of the cost of the phone, or 0.0795 (cost of phone). If we call the cost of the phone C, we can write the equation: Combine like terms, C + 0.0795C = 505.40 Divide to solve for C, 1.0795C = 505.40 C = $468.18The pre-tax cost of the phone was $468.18. |
Section PF.3 – Answers to You Try Problems
PF.3.A
a. $97.98
b. $62.90
