Problema Solution
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 provided by our tutors
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