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16 September, 19:02

Sheila wants to deposit $2,145 into savings accounts at three different banks: Bank of the US, 7/4 Bank, and Catch Bank. She will deposit five times as much into Catch Bank as 7/4 Bank because they offer a higher interest rate. She also expects the Bank of the US deposit to be 30% of the total of the other two deposits. How much will Sheila deposit into the Bank of the US savings account?

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  1. 16 September, 22:41
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    Let x = deposit for Bank of US; y = deposit for 7/4 Bank and z = deposit for Catch Bank. Since we have 3 unknowns, we have to formulate 3 independent equations from the problem statement.

    She will deposit five times as much into Catch Bank as 7/4 Bank = > z = 5y

    Bank of the US deposit to be 30% of the total of the other two deposits = >

    x = 0.3 (y+z)

    Total deposit = > $2145 = x + y + z

    There, we have formulated three. Let's assign these equations:

    Eq. 1: z = 5y

    Eq. 2: x = 0.3 (y+z)

    Eq. 3: $2145 = x + y + z

    Substitute Eq 1 to Eq 2, we get an equation for x in terms of y. This would be Eq. 4. Then, we substitute Eq 4 to Eq 3, to solve for y.

    Eq. 1 to Eq. 2:

    x = 0.3 (y + 5y) = 0.3 (6y)

    x = 1.8y = > Eq. 4

    Eq 4 to Eq 3:

    $2145 = 1.8y + y + 5y = 7.8y

    y = $2145/7.8 = $275

    Substitute y to Eq. 4 to solve for x:

    x = 1.8y = 1.8 ($275) = $495

    Substitute y to Eq 1 to solve for z:

    z = 5y = 5 ($275) = $1375

    Let's counter-check if we got the right answers

    $2145 = x + y + z = $495 + $275 + $1375

    $2145 = $2145 (Correct)

    Thus, these are the deposits for each bank:

    Bank of US: $495

    7/4 Bank: $275

    Catch Bank: $1375
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