Question

Joe paid $100 to join a health club and $50 a month to use the club. Bill paidnothing down to join the health club and $70 a month to use the club. In how manymonths will they have paid the same amount of money to their health clubs.

Answer 1

after 5 moths Joe and Bill will have paid the same amount

Explanation

Step 1

Joe paid $100 to join a health club and $50 a month to use the club

let

x represents the number of months

then

after x months joe has paid:

$\text{total}=100+50x$

Now, for Bill

Bill paid nothing down to join the health club and $70 a month to use the club

after x months bill has paid:

$\text{total}_b=70x$

Step 2

months will they have paid the same amount of money

it menas total 1= total 2

$\begin{gathered} \text{total}_j=total_{bi} \\ 100+50x=70x\text{ equation(1)} \end{gathered}$

Step 3

solve the equation

$\begin{gathered} 100+50x=70x \\ \text{subtract 50x in both sides} \\ 100+50x-50x=70x-5x \\ 100=20x \\ \text{divide both sides by 20} \\ \frac{100}{20}=\frac{20x}{20} \\ 5=x \end{gathered}$

so, the answer is

after 5 moths Joe and Bill will have paid the same amount