$5,000 is invested at 3% interest. how much money must be invested at 5% interest so that the total interest from the two investments is $275 after one year?
a) $2,000
b) $2,500
c) $3,000

Option (b)  

Explanation:

In the given problem, an amount of $5000 was invested at the interest rate of 3%.  

Hence forth, 3% interest on 5,000 = = 150

275 (the total amount wanted) - 150 (from initial investment)= 125  

Let X be the money must be invested to attain the objective  

Therefore, X (5%) =125  

That implies X (0.05)= 125  

X=  

which gives, X=2500  

hence it is in need to invest 2500 at 5% to get the additional 125  

therefore, 125 + 150= 275 .

a negative exponent is translated as follows:

so, we have