6. (10 points) Suppose that Ashley is gifted $5000 in bonds from family members.

Question

6. (10 points) Suppose that Ashley is gifted $5000 in bonds from family members. The money is distributed among 3 different bond types for a period of 1 year: Bond A earns 1% simple interest, Bond B earns 1.5% simple interest, and Bond C earns 2% simple interest. The total interest earned is S90. And, the total invested in Bond B is twice what was invested in Bond A. Set up a system of linear equations which can be used to determine how much money was invested in each bond type. Make sure you define what your variables represent. You do not need to solve your syste of equations.

Explanation / Answer

6. Let $ x be invested in type A bonds and $ y be invested in type C bonds. Then, the amount invested in type B bonds is $ 2x. Hence x+2x+y = 5000 or, 3x+y = 5000…(1)

Further, interest for 1 year on the types A,B,C bonds are x*1% = x/100, 2x*1.5% = 3x/100 and y*2% = 2y/100 respectively. Hence, x/100 + 3x/100+2y/100 = 90 or, (4x+2y)/100 = 90 or, 4x+2y = 9000 so that 2x+y = 4500…(2).

On subtracting the 2nd equation from the 1st   equation, we get (3x+y)-(2x+y) = 5000=4500 or, x = 500. Then 2x = 1000 and y = 5000-3x = 5000-1500 = 3500. Thus, the amounts invested in type A,B,C bonds are $ 500, $ 1000 and $ 3500 respectively.

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