Investments

Question

Two investments totaling $56,500 produce an annual income of $1835.  One investment yields 4% per year, while the other yields 3% per year.  How much is invested at each rate?

Answer 1

FIRST EQUATION (we know that the two investments add up to $56,500)

X + Y = 56,500

 

SECOND EQUATION (we know that one investment makes 4% and one makes 3% and the total adds up to $1835)

.04X + .03Y = 1,835

 

Now simplify the second equation.  First, multiply both sides by 25 so that we have 1X, just like in the first equation.

25(.04X + .03Y) = 25 * 1,835

X + .75Y = 45,875

 

Next, multiply both sides by -1 so that the 1X becomes -1X, which will allow us to subtract the X from the first equation and only have to deal with one variable, the Y.

 

-1(x + .75Y) = -1*45,875

-X -.75Y = -45,875

 

Now take the first equation and subtract the second equation from it:

X + Y = 56,500

-X -.75Y = -45,875

.25Y = 10625

 

Solve for Y by dividing both sides by .25.

Y = 42500

 

Solve for X by plugging the value of Y into the first equation.

X = 14100

 

Hope this helps Jen!  Let me know if you have any questions.