Question

The expressions you provided represent the account balances for Grace and the tennis account. To find when they have the same balance, set the two expressions equal to each other and solve for x:

10 - 2.5x = 10 + 100 + 2.5 + 85 - x

Answer 1

To find when two account balances are equal, we solved the equation 10 - 2.5x = 197.5 - x by simplifying and rearranging to find x = 125.

Step-by-step explanation:

The question provided is asking us to solve an equation wherein two expressions representing account balances are set equal to each other. To find the point at which they have the same balance, we solve for x. The expressions given are 10 - 2.5x and 10 + 100 + 2.5 + 85 - x. Combining like terms and then solving for x gives us a simple linear equation to work with.

First, let's simplify the right side of the equation:

10 + 100 + 2.5 + 85 - x becomes 197.5 - x.

Setting the two expressions equal to each other, we have:

10 - 2.5x = 197.5 - x

Rearranging and solving for x:

2.5x - x = 197.5 - 10 which simplifies to 1.5x = 187.5

Dividing both sides by 1.5, we find that x = 125. Therefore, x equals 125 when both account balances are equal.