simple interest?

Question

Fran receives $274 per year in simple interest from investing $3200 . Part is invested at 7% part at 8%and part at 9%. There is $1000 more invested at 9% than at 8%. Find the amount invested at 9%.

Answer 1

Given:

N = amount at 9%
E = amount at 8%
S = amount at 7%

E= N - 1,000
N + E + S = 3,200
0.09N + 0.08E + 0.07S = 274

Solution:

Replace E with "N - 1,000" in the first two equations and simplify them:

N + (N - 1,000) + S = 3,200
0.09N + 0.08(N - 1,000) + 0.07S = 274

2N + S - 1,000 = 3,200
0.17N + 0.07S - 80 = 274

2N + S = 4,200
0.17N + 0.07S = 354

Multiply all terms in the first equation by 0.07

0.14N + 0.07S = 294

Subtract these values from the second simplified equation

0.03N = 60

Divide each side of the equation by 0.03

N = 2,000

Substitue 2,000 for N in E= N - 1,000

E = 2,000 - 1,000
E = 1,000

Substitute the values of N and E in N + E + S = 3,200

2,000 + 1,000 + S = 3,200
S = 200