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)

the answer is vanilla

step-by-step explanation:

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.