Question

1. a professional carpet - cleaning service charges $30 plus $2.50 per hour to clean carpets. if your total bill is $119.25, how many hours did it take the company to clean the carpets?

a) state a variable to represent the unknown quantity. state an expression to represent any other unknown quantity. (4 points)
b) develop an equation that can be used to solve the problem. (2 points)
c) solve the problem. (4 points)

1. a company decreased its workforce by 35%. if there are now 78 employees remaining, how many employees were there before the layoffs?

a) state a variable to represent the unknown quantity. state an expression to represent any other unknown quantity. (4 points)
b) develop an equation that can be used to solve the problem. (2 points)
c) solve the problem. (4 points)

Explanation:

Question 11

Step1: Define variable

Let $h$ be the number of hours. The fixed - charge is $30$ and the charge per hour is $25.50$, so the total cost $C = 30+25.5h$.

Step2: Set up the equation

We know that $C = 119.25$. So the equation is $30 + 25.5h=119.25$.

Step3: Solve the equation

Subtract 30 from both sides:
$25.5h=119.25 - 30$
$25.5h=89.25$
Then divide both sides by 25.5:
$h=\frac{89.25}{25.5}=3.5$

Step1: Define variable

Let $x$ be the number of employees before the lay - offs. The number of remaining employees is $(1 - 0.35)x$ since the workforce decreased by 35%.

Step2: Set up the equation

We know that the number of remaining employees is 78. So the equation is $(1 - 0.35)x=78$.

Step3: Solve the equation

Since $1- 0.35 = 0.65$, the equation becomes $0.65x=78$.
Divide both sides by 0.65:
$x=\frac{78}{0.65}=120$

Answer:

a) Let $h$ be the number of hours to clean the carpets. There are no other unknown quantities to express in a non - trivial way.
b) The equation is $30 + 25.5h=119.25$.
c) The number of hours is $3.5$.

Question 12