Question

1. a student received a coupon for 17% off the total purchase price at a clothing store. let b be the original price of the purchase. use the expression b - 0.17b for the new price of the purchase. write an equivalent expression by combining like terms.
2. kirana buys boxes of crackers that each have the same cost, c. she represents the cost of 3 boxes of cheese crackers, 2 boxes of poppy seed crackers, and 2 boxes of plain crackers with the expression 3c + 2c + 2c. what equivalent expression can represent the cost?
3. a student received a coupon for 14% off the total purchase price at a clothing store. let c be the original price of the purchase. the expression c - 0.14c represents the new price of the purchase. write an equivalent expression to show another way to represent the new price.
4. a farmer recently sold a large plot of land. the sale decreased his total acreage by 8%. let v be the original acreage.

a. find two equivalent expressions that will give the new acreage.
b. use the expressions to describe two ways to find the new acreage.

1. an art teacher enlarged the area of a copy of a painting by 49%. let d represent the area of the original painting. the expression d + 0.49d is one way to represent the area of the new painting. write two additional expressions that will give the area of the new painting.

Explanation:

Problem 8

Step1: Identify remaining percentage

New price = $100\% - 17\% = 83\%$ of original

Step2: Write equivalent expression

$0.83b$

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Problem 10

Step1: Identify remaining percentage

New price = $100\% - 14\% = 86\%$ of original

Step2: Write equivalent expression

$0.86c$

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Problem 9

Step1: Combine like terms

$3c + 2c + 2c = (3+2+2)c$

Step2: Calculate sum of coefficients

$7c$

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Problem 11a

Step1: Subtract 8% from original

$v - 0.08v$

Step2: Calculate remaining percentage

$1 - 0.08 = 0.92$, so $0.92v$

Problem 11b

Step1: Simplify the expressions

$v - 0.08v = 0.92v$

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Problem 12

Step1: Factor out original area

$d(1 + 0.49)$

Step2: Simplify the sum

$1 + 0.49 = 1.49$, so $1.49d$

Answer:

1. $\boldsymbol{0.83b}$
2. $\boldsymbol{0.86c}$
3. $\boldsymbol{7c}$
4. a. $\boldsymbol{v - 0.08v}$ and $\boldsymbol{0.92v}$

b. $\boldsymbol{0.92v}$

1. $\boldsymbol{1.49d}$ and $\boldsymbol{d(1 + 0.49)}$