Solving word problem of compound inequalities

Question

A person inherits $14,000 with the stipulation that for the first year the money must be invested in two stocks paying 6% and 7% annual interest, respectively. What is the greatest amount that can be invested at 6% if the total interest earned for the year must be at least $940?

Answer 1

X+Y = 14000

 

0.06X + 0.07Y = 940

 

6X + 7Y = 94000

 

6X + 7(14000 - X) = 94000

 

6X + 98000 - 7X = 94000

 

-X = -4000

X=4000

 

Y=10000