Find 3 variables and the 3 linear equations

A man has invested $235,000 in 3 properties. One earns 12% another 10% and the last earns 8%. His total annual income is $22,500. The amount at 8% is twice the investment at 12%. Define 3 variables and 3 linear equations.
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1 Answer

Let variables A, B, C be the investment amounts on each property.

The annual returns are 0.12A, 0.10B, 0.08C.

Total Investment: A+B+C=235000 (equation 1).

Total returns: 0.12A+0.10B+0.08C=22500 (equation 2).

C=2A (equation 3) so 0.08C=0.16A.

Therefore: 3A+B=235000, substituting for C. So B=235000-3A and 0.10B=23500-0.3A.

0.28A+0.10B=22500, substituting for 0.08C and 0.28A+23500-0.3A=22500, substituting for 0.10B.

Therefore, 0.02A=1000 and A=$50000.

B=235000-150000=$85000 and C=$100000.

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