word problems in algebra

Question

An algebra student has won $510,000 in a lottery and wishes to deposit it in savings accounts in two financial institutions. One account pays 9% simple interest, but deposits are insured only to $250,000. The second account pays 6.2% simple interest, and deposits are insured up to $500,000. Determine whether the money can be deposited so that it is fully insured and earns annual interest of $39,120.

1. The money can be fully insured and earn annual interest of $39,120.
2. The money cannot be fully insured and earn annual interest of $39,120.    

Answer 1

X and Y are the amount invested into each account...

0.09X + 0.062Y = 39120

X+Y = 510000

0.09X + 0.062 ( 510000 - X) = 39120

0.09X + 31629 - 0.062X = 39120

0.028X = 7291

x = 267,535.70 <-- rounded to nearest penny

which forces

y=242,464.30

The money cannot be fully

insured and earn annual interest of $39,120.