Question

Damien wants to deposit $1200 into savings accounts at three different banks: Bank of Chance, Merchant Bank, and Utopian Financing. He will deposit three times as much into Merchant Bank as Bank of Chance because they offer a higher interest rate. He also expects the Utopian Financing deposit to be only 20% of the total of the other two deposits. How much will Damien deposit into the Utopian Financing savings account?

$240
$250
$200
$750
Please help.
If you explain how you got the answer i will give you a medal

Answer 1

No. I'm not sure how to do that

Answer 2

@johnweldon1993 can you help??

Answer 3

Hey sorry I wasn't on yesterday...but in case you still need the help

Think of it like this...assign every bank a variable

Let

Bank of Chance = C
Merchant Bank = M
Utopian Financing = U

We know he is going to make deposit 1200 total into these 3 banks...so

\[\large C + M + U = 1200\]

"He will deposit three times as much into Merchant Bank as Bank of Chance "

This means

\[\large 3M = C\] there will be 3 times more than C

"He also expects the Utopian Financing deposit to be only 20% of the total of the other two deposits"

So the total of the other 2 deposits are C + M

And f U will be 20% of that...we have

\[\large .20(C+M)\]

So now, we have 3 equations

\[\large C + M + U = 1200\]
\[\large 3M = C\]
\[\large U = .20(C + M)\]

Focus on the last 2 equations first...

We know that C = 3M so plug that into the last equation

\[\large U = .20(3M + M)\]
\[\large U = .20(4M)\]

Now notice....the first equation....we have

\[\large C + M + U = 1200\]

Well we now know that U = .20(4M) and that C = 3M

lets plug all that in

\[\large 3M + M + (.20(4M)) = 1200\]
\[\large 4M + (.20(4M) = 1200\]
\[\large 4M + \frac{4}{5}M = 1200\]
\[\large \frac{24}{5}M = 1200\]
\[\large M = 250\]

He will deposit 250 into M

Now that you know that...plug in that into the 2nd equation

\[\large 3M = C\]
\[\large 3(250) = C\]
\[\large 750 = C\]

So 750 into chance..

and finally for U...we know that

\[\large C+M+U = 1200\]
\[\large 750 + 250 + U = 1200\]
\[\large 1000 + U = 1200\]
\[\large U = 200\]

He will deposit 200 into Utopian

Answer 4

Thank you!! i'm still working on this module so this helps a lot. and i have a different scenario about taxes and things. could you maybe help with that too? @johnweldon1993