Katie invested a total of $8000, part at 4% simple interest and part at 5% simple interest. At the end of 1 year, the investments had earned $371 interest. How much was invested at each rate?

Answer 1

We have 2 unknowns, therefore we need 2 equations to solve this.

Let x = amount invested at 4% rate

y = amount invested at 5% rate

Eq. I x + y = 8000

Eq. II: .04x + .05y = 371

We can solve this by using either the substitution or the elimination method. Let's use the substitution method:

x + y = 8000 Eq. I

x = 8000 - y subtract y from both sides to isolate the x

.04x + .05y = 371 Eq. II

.04(8000 - y) + .05y = 371 substitute (8000 - y) for x

320 - .04y + .05y = 371 simplify

-.04y + .05y = 371 - 320 combine like-terms by subtracting 320 from both sides

.01y = 51 simplify

y = 51/.01 divide both sides to isolate y

y = 5100 solve for y

Using this value for y we can solve for x in Eq. I:

x + y = 8000 Eq. I

x = 8000 - y

x = 8000 - 5100 substituting 5100 for y

x = 2900 solve for x

Therefore, the answers are x = $2900 and y = $5100.

Hope this helps!