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Choco pies are cookies made from chocolate (c), sugar (s), and flour (f). Chocolate costs $5 per pound, sugar costs $3 per pound, and flour costs $2 per pound. You spend $50 on 18 pounds of food and buy twice as much flour as sugar. Calvin wants to invest $12,000 in deposits. For tax purposes, he wants his total interest to be $600. He wants to put $1000 more in a 2-year deposit than in a 1-year deposit and invest the rest in a 3-year deposit. How much money should he invest in each deposit?

Respuesta :

Answer:

The amount of money he should invest in a 1-year deposit is  $3,333.333

The amount of money he should invest in a 2-year deposit is $4,333.333

The amount of money he should invest in a 3-year deposit is $8666.67

Step-by-step explanation:

The given parameters are;

Total investment = $12,000

Total interest = $600

Interest rate = r

Amount invested in a 2-year deposit, B = $1,000 + Amount invested in a 1-year deposit, A

Amount invested in a 3-year deposit, C = $12,000 - (A + B)

C = 12000 - 2·B + 1000 = 13000 - 2·B

∴ A + B + C = $12,000

A×r + 2×r×B + 3×r×C = $600

∴ r×(A + 2·B + 3·C) = $600

r×(12000 + B + 2·C) = $600

B = A + 1000

∴ r×(B - 1000 + 2·B + 3·(13000 - 2·B) = $600

r×(B - 1000 + 2·B + 3·(13000 - 2·B) = $600

r×(38000 - 3·B) = $600

∴B + 2·C = -3·B

4·B = 2·C

C = 2·B

Hence;

B - 1000 + B + 2·B = $12,000

3·B = 13,000

∴ B = 13000/3 = [tex]\$4,333\tfrac{1}{3}[/tex] = $4,333.333

B = A + 1000

∴ A = B - 1000 = [tex]\$3,333\tfrac{1}{3}[/tex] = $3,333.33

C = 2×B = [tex]\$8,666\tfrac{2}{3}[/tex] = $8666.67

Therefore;

The amount of money he should invest in a 1-year deposit =  $3,333.333

The amount of money he should invest in a 2-year deposit = $4,333.333

The amount of money he should invest in a 3-year deposit = $8666.67.

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