Respuesta :
For the given problem:
Let the balances of the saving accounts be (x) and (y)
Leah has two savings accounts with balances totaling $8,000
so,
[tex]x+y=8000\rightarrow(1)[/tex]She withdrew 15% from one and 40% from the other. If she has $6,350 remaining in the accounts
So, The remaining from the accounts will be (1 - 15%) and ( 1 - 40%)
that will give the decimals: 0.85 and 0.6
so, we can write the following equation:
[tex]0.85x+0.6y=6350\rightarrow(2)[/tex]Now, solve the equations (1) and (2) to find (x) and (y)
From equation (1):
[tex]y=8000-x\rightarrow(3)[/tex]Substitute with (y) from equation (3) into equation (2)
[tex]0.85x+0.6\cdot(8000-x)=6350[/tex]Solve the equation to find (x):
[tex]\begin{gathered} 0.85x+0.6\cdot8000-0.6x=6350 \\ 0.85x-0.6x+4800=6350 \\ 0.25x=6350-4800 \\ 0.25x=1550 \\ x=\frac{1550}{0.25}=6200 \end{gathered}[/tex]Substitute with (x) into equation (3) to find (y)
[tex]y=8000-6200=1800[/tex]So, the larger account = x = 6200
and the smaller account = y = 1800
Now, we will answer the question, how much money did she withdraw from the account with the larger balance?
so, the answer will be: 15% of x = 0.15 * 6200 = 930
So, the answer will be $930
