Chapter 8.8, Problem 38IP

To determine

Write and solve an equation to find the number of months for which the two gym have the same cost.

Answer to Problem 38IP

  $45+21x=60+18x$ ; After 5 months, the two GYM have same cost.

Explanation of Solution

Given:

Sumi is considering two gyms. Gym A has a onetime membership fee of $45 and costs $21 per month. Gym B has a one − time membership of $60 and costs $18 per month. Write and solve an equation to find the number of months for which the two gym have the same cost. Explain how your solution relates to the problem situation.

Concept Used:

Translate the conditions given into an equation.

Let x be represent as the number of month.

Gym A has a onetime membership fee of $45 and costs $21 per month: $\$(45+21x)$

Gym B has a one − time membership of $60 and costs $18 per month: $\$(60+18x)$

Write and solve an equation to find the number of months for which the two gym have the same cost.

The required equation: $45+21x=60+18x$ when two GYM have same cost.

Calculation:

The required equation: $45+21x=60+18x$ when two GYM have same cost.

Now solve for x, the number of months.

  $\begin{array}{l}45+21x=60+18x\\ 45-45+21x=60-45+18x\text{[}\text{Subtract}45\text{from}\text{both}\text{sides}\text{]}\\ 21x=15+18x\\ 21x-18x=15+18x-18x\text{[}\text{Subtract}18x\text{from}\text{both}\text{sides}\text{]}\\ 3x=15\\ \frac{3x}{3}=\frac{15}{3}\text{[}\text{Divide}\text{both}\text{sides}\text{by}3\text{]}\\ x=5\end{array}$

Thus, after 5 months the cost of two GYM will be same.