Bruce is working on paying back some money he borrowed from a friend by making monthly payments. Bruce has given the friend a down payment of $257, and each month he will pay the friend $45. If the total amount loaned to Bruce is $347, what equation can be used to represent the number of months it will take Bruce to pay back all of the money? Represent the number of months as the variable x .

To create an equation representing this scenario, we have to have an equation equaling 347, which is the total amount in $ that Bruce owes his friend.

347 =

We know that Bruce made a downpayment of 257, so that must go on the right side of the equation since that is part of what bruce paid back of the total $347.

347 = 257 + ?

Now we need to create a term representing the rest of the money Bruce will pay back. X represents the number of months Bruce will pay his friend $45. If the number of months is multiplied by 45, we will get the amount of money Bruce paid after his initial downpayment of $257. Put this into our equation to make the equation true.

347 = 257 + 45x

Now, let's solve for x.

Subtract 257 on both sides.

90 = 44x

Divide by 45 on both sides.

2 = x

Bruce must pay $45 dollars to his friends once a month for 2 months, which means he must pay $90 after the downpayment of $257. We can check our answer by substituting 2 into our equation.

347 = 257 + 45(2)

Multiply 45*2.

347 = 257 + 90

Add 257 and 90.

347 = 347

Our equation is true, so we know that the equation 347 = 257 + 45x accurately represents this scenario and that x = 2.