Benjamin wants to join a gym in his neighborhood. It costs 20 dollars for the first subscription plus a monthly fee of 12 dollars. If Benjamin has 152 dollars to spend, write and solve an equation to find the number of months he can use the gym.
We’re asked to write and solve an equation. And we are finding the number of months. So we are solving for the number of months. So we can let the number of months be equal to 𝑥. That will be our variable that we will be solving for.
So let’s go ahead and look at what we’re given. Benjamin has a total of 152 dollars to spend. The first subscription cost 20 dollars. And then there’s a monthly fee of 12 dollars after that.
Let’s begin with the monthly fee. It is 12 dollars per month. So we need to take however many months he is there and multiply it by 12. So we can represent the monthly fee by 12 times 𝑥.
But first he had to pay his first subscription of 20 dollars. And then after that, he pays 12 dollars times however many months he is there. So the cost to use the gym would be 20 dollars plus 12 times 𝑥. And we need to set it equal to 152 dollars because that is the amount of money he has. It can’t be more than that. And we also say it’s not going to be less than that because he wants to know the number of months he can use the gym.
Essentially, what is the- the largest number of months that he can use the gym? So we are just setting it equal to 152. So this would be our equation. Now we need to solve for 𝑥.
So the first thing that we need to do is subtract 20 from both sides of the equation. On the left-hand side of the equation, the 20s cancel. And on the right, 152 minus 20 is 132.
So now how to solve for 𝑥, we need to get rid of the 12. And 12 is being multiplied to 𝑥. So the opposite of multiplying would be to divide. So we divide both sides of the equation by 12. And we find that 132 divided by 12 is 11. So 𝑥 represented the months. So that means he could use the gym for 11 months, almost a whole year.
Our equation could be written as 12𝑥 plus 20 equals 152. Or we could have written it as 20 plus 12𝑥 equals 152. It wouldn’t matter. And in solving this equation, we found that the number of months that Benjamin could use the gym would be 11 total months.