Question

1. gym a and gym b charge different prices for a monthly gym membership. the equation $y=25x$ represents the total cost, y, in dollars, for x months of membership at gym a. the graph below represents the total cost for the same type of membership at gym b. what is the unit rate for the price of membership per month at each gym?gym a ________ per monthgym b ______ per month7. company a and company b charge different prices for printing posters. the equation $y=1.85x$ represents the total cost, y, in dollars, for printing x posters at company a. the graph below represents the total cost for printing the same posters at company b. what is the unit rate for the price of printing, per poster, at each company?company a$__________ per postercompany b$________ per poster

Explanation:

Step1: Identify Gym A's unit rate

The equation for Gym A is $y=25x$, where $y$ is total cost and $x$ is months. The coefficient of $x$ is the unit rate.
Unit rate (Gym A) = $25$ dollars per month

Step2: Calculate Gym B's unit rate

Use the point $(6,150)$ from the graph. Unit rate = $\frac{\text{Total Cost}}{\text{Months}}$
$\text{Unit rate (Gym B)} = \frac{150}{6} = 25$ dollars per month

Step3: Identify Company A's unit rate

The equation for Company A is $y=1.85x$, where $y$ is total cost and $x$ is posters. The coefficient of $x$ is the unit rate.
Unit rate (Company A) = $1.85$ dollars per poster

Step4: Calculate Company B's unit rate

Use the point $(20,40)$ from the graph. Unit rate = $\frac{\text{Total Cost}}{\text{Posters}}$
$\text{Unit rate (Company B)} = \frac{40}{20} = 2$ dollars per poster

Answer:

Gym A: $\boldsymbol{25}$ dollars per month
Gym B: $\boldsymbol{25}$ dollars per month

Company A: $\boldsymbol{1.85}$ dollars per poster
Company B: $\boldsymbol{2}$ dollars per poster