Maricopa's Success scholarship fund receives a gift of $ 185000. The money is invested in stocks, bonds, and CDs. CDs pay 5 % interest, bonds pay 5.5 % interest, and stocks pay 11.3 % interest. Maricopa Success invests $ 30000 more in bonds than in CDs. If the annual income from the investments is $ 13115 , how much was invested in each account?

Maricopa Success invested $ in stocks.

Maricopa Success invested $ in bonds.

Maricopa Success invested $ in CDs.

Maricopa Success invested $55,000 in stocks

Maricopa Success invested $80,000 in bonds

Maricopa Success invested $50,000 in CDs

Step-by-step 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)

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step-by-step explanation:

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