Question

Mia wants to deposit $3,886 into savings accounts at three different banks: Bank of the US, 7/4 Bank, and Catch Bank. She will deposit three times as much into Bank of the US as 7/4 Bank because they offer a higher interest rate. She also expects the Catch Bank deposit to be 45% of the total of the other two deposits. How much will Mia deposit into the Catch Bank savings account? (5 points) $670 $1,206 $1,340 $2,010

Answer 1

A = deposit at US bank

b = deposit at 7/4 bank

c = deposit at Catch bank.

we know her total is 3886, thus  a + b + c = 3886.

now, we know whatever "b" is, the amount at US bank, "a", is 3 times that much, thus a = 3b.

(3b) + b + c = 3886.

whatever% of anything, is just (whatever/100) * anything.

we know Catch bank gets 45% of whatever the sum of the other two is, well, US bank gets "3b", 7/4 bank gets "b", their total is 3b + b = 4b, and Catch bank gets 45% of that, (45/100) * 4b

$\bf \stackrel{US~bank}{3b}~+~\stackrel{7/4~bank}{b}~+~\stackrel{Catch~bank}{\frac{45}{100}(4b)}~=~3886 \\\\\\ 4b+\cfrac{9}{5}b=3886\impliedby \textit{let's multiply both sides by }\stackrel{LCD}{5} \\\\\\ 20b+9b=19430\implies 29b=19430\implies b=\cfrac{19430}{29}\implies b=670$

how much is it for the Catch bank?  well, (45/100) * 4(670).