Solve the problem.The formula A = P + Prt represents the value, A, of an investment of P dollars at a yearly simple interest rate, r, for t years. The equation to model the value, A, of an investment of $54 at 9.26% for t years is given by A = 54 + 5t. The equation to model the value, A, of an investment of $84 at 2.38% for t years is given by A = 84 + 2t. Assuming A has the same value, the given equations form a system of two linear equations. Solve this system using an algebraic approach and interpret your answer.
Answer
A
t = 5The two investments will reach the same value in 5 years.
B
t = 20The two investments will reach the same value in 20 years.
C
t = 1000The two investments will reach the same value in 1000 years.
D
t = 10The two investments will reach the same value in 10 years.
Explanation
Set the two investment values equal: 54 + 5t = 84 + 2t. Subtract 2t and 54 from both sides to get 3t = 30, so t = 10. The investments will reach the same value in 10 years, which is choice d.
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