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.


a.t = 5. The two investments will reach the same value in 5 years.

c.t = 1000. The two investments will reach the same value in 1000 years.

b.t = 20. The two investments will reach the same value in 20 years.

d.t = 10. The two investments will reach the same value in 10 years.