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?

Answer 1

Let's start by defining some variables:

Let c = Amount deposited in Bank of Chance
Let m = Amount deposited in Merchant Bank
Let u = Amount deposited in Utopian Financing

Answer 2

x+y+z = 1200
x = 3y
z = 0.2(x+y) = 0.2(4x)

Answer 3

Because we know the total amount is $1200, our first equation will be:

c+m+u = 1200

Answer 4

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

How would that be interpreted?

Answer 5

What you want to note here is that three times as much goes into Merchant Bank. So Merchant Bank will be 3 times what Bank of Chance will be. You can express that like this:

3c=m

Answer 6

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

Answer 7

So that means:

u=20%(c+m)

Answer 8

Now, we don't work with percents, so we need to turn that into a decimal.

u=.2(c+m)

Answer 9

So the equations we're left with are:

c+m+u=1200
3c=m
u=.2(c+m)

Answer 10

From here, let's plug in what we know from the second and third equations into the first equation:

c+m+u=1200

Well, we know that m=3c and we know that u=.2(c+m)

Answer 11

So we're really looking at:

c+(3c)+.2(c+(3c))=1200

Answer 12

c+(3c)+.2(c+(3c))=1200
4c + .2(4c) = 1200
4c + .8c = 1200
4.8c=1200
/4.8 /4.8

c=250

Answer 13

And, if we know c = 250 then we can figure out m, because m = 3c

m=3(250)
m=750

Answer 14

And now that we know those two amounts and we know the total has to be 1200, we can use that first equation:

c+m+u=1200
250+750+u=1200
1000+u=1200
-1000 -1000
u=200

Answer 15

So finally:

c=$250
m=$750
u=$200

And your teacher will probably want you to answer the question in a complete sentence. :)