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.