Question

Rosa has $117 in her savings account and $95 in her checking account. Each week she will put $21 into her savings account and $25 into her checking account. Complete the equation that can be used to find the number of weeks, x, until Rosa has the same amount of money in both accounts.

Answer 1

• 5.5 weeks

Explanation:

Given

Initial balance

• Savings account = $117
• Checking account = $95

Added amount per week

• Savings account = $21
• Checking account = $25

If number of weeks is x, then required equation is

• 117 + 21x = 95 + 25x

Solving for x

• 25x - 21x = 117 - 95
• 4x = 22
• x = 22/4
• x = 5.5

The answer is 5.5 weeks

Answer 2

It will take Rosa 5 and a half (5.5) weeks to have the same amount of money in both accounts.

Explanation:

For this problem, we will have to set two expressions equal to each other. The first expression will represent Rosa's saving account, which already has $117 in it. Every week (
`x`), she adds $21 to her savings account:

`21x+117`

The second expression will represent Rosa's checking account. Rosa's checking account already has $95 in it. Every week (
`x`), she adds $25 to her checking account:

`25x+95`

Now that we have our two expressions, set them equal to each other. This is our equation that will be used to find the number of weeks (
`x`) it takes until Rosha has the same amount of money in both accounts:

`21x+117=25x+95`

Subtract
`21x` from both sides of the equation:

`117=4x+95`

Subtract
`95` from both sides of the equation:

`22=4x`

Divide both sides of the equation by the coefficient of
`x`, which is
`4`:

`5.5=x`

`x=5.5`

So it will take five and a half weeks for her accounts to have the same amount of money.

_

Check your work by substituting
`5.5` into the initial equation:

`21(5.5)+117=25(5.5)+95`

`115.5+117=137.5+95`

`232.5=232.5`

Since the accounts have the same amount, the answer is correct!