Linear problem/question

Question

BIll inherited $25,000 and invested part of it in a money market account, part in bonus bonds and part in a mutual fund. After one year, he received a total of $1,620 in simple interest from the three investments. The money market paid 6% annually, the bonds paid 7% annually, and the mutual fund paid 8% annually. There was $6000 more invested in the bonds than the mutual funds.

• Set up and solve a system of equations to find the amount Tyrone invested in each category.

Answer 1

x + y + z = 25000

0.06x + 0.07y + 0.08z = 1620

y = z + 6000

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x + (z + 6000) + z = 25000

x + 2z + 6000 = 25000

x + 2z = 19000

x = 19000 - 2z

0.06x + 0.07y + 0.08z = 1620

0.06 (19000 - 2z) + 0.07( z + 6000) + 0.08z = 1620

1140 - 0.12z + 0.07z + 420 + 0.08z = 1620

0.03z + 1560 = 1620

0.03z = 60

3z = 6000

z = 2000

x = 19000 - 2(2000) = 19000 - 4000 = 15000

y = 2000 + 6000 = 8000

15000 in market account

8000 in bonds

2000 in mutual funds