Answer:
It will take Rosa 5 and a half (5.5) weeks to have the same amount of money in both accounts.
Step-by-step 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 ([tex]x[/tex]), she adds $21 to her savings account:
[tex]21x+117[/tex]
The second expression will represent Rosa's checking account. Rosa's checking account already has $95 in it. Every week ([tex]x[/tex]), she adds $25 to her checking account:
[tex]25x+95[/tex]
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 ([tex]x[/tex]) it takes until Rosha has the same amount of money in both accounts:
[tex]21x+117=25x+95[/tex]
Subtract [tex]21x[/tex] from both sides of the equation:
[tex]117=4x+95[/tex]
Subtract [tex]95[/tex] from both sides of the equation:
[tex]22=4x[/tex]
Divide both sides of the equation by the coefficient of [tex]x[/tex], which is [tex]4[/tex]:
[tex]5.5=x[/tex]
[tex]x=5.5[/tex]
So it will take five and a half weeks for her accounts to have the same amount of money.
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Check your work by substituting [tex]5.5[/tex] into the initial equation:
[tex]21(5.5)+117=25(5.5)+95[/tex]
[tex]115.5+117=137.5+95[/tex]
[tex]232.5=232.5[/tex]
Since the accounts have the same amount, the answer is correct!
