Answer:
Maricopa Success invested $55,000 in stocks
Maricopa Success invested $80,000 in bonds
Maricopa Success invested $50,000 in CDs
Explanation:
Let S denotes stocks, B denotes bonds and C denotes CDs.
Maricopa's Success scholarship fund receives a gift of $185,000 which she invests in stocks. bonds, and CDs.
Mathematically,
S + B + C = 185,000 eq. 1
Money is invested in stocks at interest = 11.3% = 0.113
Money is invested in bonds at interest = 5.5% = 0.055
Money is invested in CDs at interest = 5% = 0.05
Annual income from the investments is $13,115
Mathematically,
0.113S + 0.055B + 0.05C = 13,115 eq. 2
Maricopa Success invests $30,000 more in bonds than in CDs.
Mathematically,
B = C + 30,000 eq. 3
Substitute the eq. 3 into eq. 1
S + B + C = 185,000
S + (C + 30,000) + C = 185,000
S + 2C + 30,000 = 185,000
S + 2C = 185,000 - 30,000
S + 2C = 155000 eq. 4
Substitute the eq. 3 into eq. 2
0.113S + 0.055B + 0.05C = 13,115
0.113S + 0.055(C + 30,000) + 0.05C = 13,115
0.113S + 0.055C + 1650 + 0.05C = 13,115
0.113S + 0.105C + 1650 = 13,115
0.113S + 0.105C = 13,115 - 1650
0.113S + 0.105C = 11,465 eq. 5
Now we have to equations and two unknowns
S + 2C = 155,000 eq. 4
0.113S + 0.105C = 11,465 eq. 5
Multiply eq. 4 by 0.113 and subract it from eq. 5
0.113S + 0.226C = 17,515
subtract it from eq. 5
0.113S + 0.105C = 11,465 eq. 5
0.113S + 0.226C = 17,515
-0.121C = -6050
0.121C = 6050
C = 6050/0.121
C = 50,000
Substitute the value of C into eq. 3
B = C + 30,000
B = 50,000 + 30,000
B = 80,000
Substitute the value of B and C into eq. 1
S + B + C = 185,000
S + 80,000 + 50,000 = 185,000
S = 185,000 - 80,000 - 50,000
S = 55,000
Therefore,
Maricopa Success invested $55,000 in stocks
Maricopa Success invested $80,000 in bonds
Maricopa Success invested $50,000 in CDs
Verification:
S + B + C = 185,000 eq. 1
55,000 + 80,000 + 50,000 = 185,000
185,000 = 185,000 (satisfied)
0.113S + 0.055B + 0.05C = 13,115 eq. 2
0.113(55,000) + 0.055(80,000) + 0.05(50,000) = 13,115
6215 + 4400 + 2500 = 13,115
13,115 = 13,115 (satisfied)
B = C + 30,000 eq. 3
80,000 = 50,000 + 30,000
80,000 = 80,000 (satisfied)