Expert: Bobby Soltani - 11/7/2005

Question
Hello:

If (5% X $1.00) + (2% X $1.00) = 3.5% X $2.00
or ($0.07/$2.00) = 3.5%
what amount multiplied by 5% plus what amount multiplied by 2% will equal 4% X $3.00?

Answers: $2.00 and $1.00
(5% X $2.00) + (2% X $1.00) = 4% X $3.00

If possible, use a non-algebraic calculation or explanation to determin the answers.

I thank you for your reply.

Answer
Hi,

what amount(x) multiplied by 5% plus what amount(y) multiplied by 2% will equal 4% X $3.00?  Here is what that looks like in equation form.

(5% * x) + (2% * y) = 4% * $3.00

We know that the total dollar amount is equal to $3.00, so we can write

x + y = 3

Now, we can solve the second equation for x, and substitute that value in for x in the first equation.  Here's how

x + y = 3
subtract y from both sides
x = 3 - y
plug 3-y in for x in the first equation.

(5% * (3 - y)) + (2% * y) = 4% * $3.00
solve for y.  For math purposes, 5% = 0.05

(0.15 - 0.05y) + 0.02y = 0.12
subtract 0.15 from both sides
-0.05y + 0.02y = -0.03
-0.03y = -0.03
divide both sides by -0.03
y = 1

Plug y = 1 into x = 3 - y to solve for x.
x = 3 - 1 = 2

So, x = $2, and y = $1

Let me know if you have any questions.

Bobby