Question

3.) You are looking at the cost of two local gyms. The first gym charges a $50 sign-up fee and charges $10 a month. The second gym charges a $30 sign-up fee and charges $12 a month. Write and solve an equation to determine after how many months the two gyms will charge the same amount

Answer 1

The cost of the first gym is given by the following equation:

`\text{cost}_1(x)=50+10\cdot x`

The cost of the second equation is given by:

`\text{cost}_2(x)=30+12\cdot x`

Where "x" is the number of elapsed months. To find an equation that determine after how many months the cost will be the same on both academies we need to make "cost1" equal to "cost2".

`\begin{gathered} \text{cost}_1(x)=\text{ cost}_2(x) \\ 50+10x=30+12x \\ 12x-10x=50-30 \\ 2x=20 \\ x=(20)/(2)=10 \end{gathered}`

The cost for the academies will be the same after 10 months.