Mary has a total of $5000 invested in two accounts. One account pays 5% and the other 8%. Her interest in the first year was $331. Write and solve a system of equations to find out how much she has invested in both accounts.

Question

Mary has a total of $5000 invested in two accounts.  One account pays 5% and the other 8%.  Her interest in the first year was $331.  Write and solve a system of equations to find out how much she has invested in both accounts.

Henry · Answer

Eq1: Po1+ Po2 = 5000

Po1*0.05*1 + Po2*0.08*1 = 331
0.05Po1 + 0.08Po2 = 331

Eq2: 5Po1 + 8Po2 = 33100
Multiply Eq1 by -5 and add Eq1 and Eq2:
-5Pol - 5Po2 = -25,000
+5Po1 + 8Po2 = 33,100
Sum: 3Po2 = 8100
Po2 = $2700
Pol = 5000-2700 = $2300.