Question

hi how do i solve this word problem?Leah has two savings accounts with balances totaling $8,000. She withdrew 15% from one and 40% from the other. If she has $6,350 remaining in the accounts, how much money did she withdraw from the account with the larger balance?

Answer 1

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,

`x+y=8000\rightarrow(1)`

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:

`0.85x+0.6y=6350\rightarrow(2)`

Now, solve the equations (1) and (2) to find (x) and (y)

From equation (1):

`y=8000-x\rightarrow(3)`

Substitute with (y) from equation (3) into equation (2)

`0.85x+0.6\cdot(8000-x)=6350`

Solve the equation to find (x):

`\begin{gathered} 0.85x+0.6\cdot8000-0.6x=6350 \\ 0.85x-0.6x+4800=6350 \\ 0.25x=6350-4800 \\ 0.25x=1550 \\ x=(1550)/(0.25)=6200 \end{gathered}`

Substitute with (x) into equation (3) to find (y)

`y=8000-6200=1800`

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