Question

table of contents > module 7: rational expressions and equations > module 7 pretest: rational expressions and equations
module 7 pretest: rational expressions and
equations
module 7 pretest: rational expressions and equations
score: 6/9 answered: 6/9
question 7
a carpet store charges $330.00 to install 60 square yards of carpet. assuming they charge the
same rate per square yard regardless of the amount of carpet installed, how much would
they charge to install 300 square yards of carpet? what is the unit price for installation per
square yard of carpet?
translate to an equation involving proportions:
they would charge $ to install 300 square yards of carpet.
$ per square yard

Explanation:

Step1: Define variables and proportion

Let \( x \) be the cost for 300 square yards. The rate per square yard is constant, so \(\frac{330}{60}=\frac{x}{300}\).

Step2: Solve for \( x \)

Cross - multiply: \( 60x = 330\times300 \). Then \( x=\frac{330\times300}{60} \). Calculate \( 330\times300 = 99000 \), and \( \frac{99000}{60}=1650 \).

Step3: Find unit price

Unit price \(=\frac{330}{60}=5.5\) dollars per square yard.

Answer:

Translate to an equation involving proportions: \(\boldsymbol{\frac{330}{60}=\frac{x}{300}}\) (where \( x \) is the cost for 300 square yards)
They would charge \(\boldsymbol{1650}\) to install 300 square yards of carpet.
\(\boldsymbol{5.5}\) per square yard