Algebra
posted by Sarah on .
an investment of 72,000 was made by a business club. the investment was split into three parts and lasted for one year. the first part of the investment earned 8% interest. the second 6% and the third 9%. total interest from the investments was $5640. the interest from the first investment was 3 times the interest from the second. find the amounts of three parts of the investment

$Xin 1st inv.
$Yin 2nd inv.
$Zin 3rd inv.
0.08X + 0.06Y + 0.09Z = $5640.
Eq1: 0.08X + 0.06Y + 0.09Z = 5640.
Eq2: X + Y + Z = 72000.
Multiply Eq1 by 100 and Eq2 by 9:
8X + 6Y + 9Z = 564000,
9X  9Y  9Z =  648000,
Add the Eqs:
X  3Y = 84,000,
0.08X = 3*0.06Y,
X = 2.25Y
Substitute 2.25Y for X:
2.25Y  3Y = 84000,
5.25Y = 84000,
Y = $16000.
X = 2.25Y = 2.25 * 16000 = $36,000.
X + Y + Z = $72000,
36000 + 16000 + Z = 72000,
Z = $20,000.