Word problem

Question

Miss Smith invested part of her savings of $28,000 at 5% annual interest and the rest at 8%. If her income from the 5% investment was 25% of her income from the 8% investment, how much did she invest at 8%?

Answer 1

Let x=the amount invested at 5%.  Then the amount invested at 8% is $28,000-x.  (For instance, if she invested 11,000 at one rate, the remainder (17,000) is 28,000-11,000).

 

The 5% investment earns 25% as much As the 8% investment, so we can set up an equation that looks like this:

 

.05x = .08(28,000-x)(1/4)

(each investment is the rate (.05 and .08) times the amount (x and 28,000-x) being invested, and the first one is 1/4 the amount of the second one).  Simplifying:

 

.05x = (2,240 - .08x)(1/4)

.05x = 560 - .02x

.07x = 560

x = 8,000.

 

the amount she invested at 8% was 28,000-x, or 20,000.

 

this checks - she made 5% of 8,000, or 400.  She made 8% of 20,000, or 1,600.  400 is one fourth of 1,600.