Question

maya and her husband are each starting a saving plan. maya will initially set aside $250 and then add $145 every month to the savings. the amount a (in dollars) saved this way is given by the function a = 145n + 250, where n is the number of months she has been saving. her husband will not set an initial amount aside but will add $485 to the savings every month. the amount b (in dollars) saved using this plan is given by the function b = 485n. let t be total amount (in dollars) saved using both plans combined. write an equation relating t to n. simplify your answer as much as possible. t =

Explanation:

Step1: Recall total is sum of A and B

Total amount \( T \) is the sum of Maya's savings \( A \) and her husband's savings \( B \). So \( T = A + B \).

Step2: Substitute A and B with their functions

We know \( A = 145N + 250 \) and \( B = 485N \). Substitute these into the equation for \( T \): \( T=(145N + 250)+485N \).

Step3: Combine like terms

Combine the \( N \)-terms: \( 145N+485N = (145 + 485)N=630N \). So \( T = 630N+250 \).

Answer:

\( T = 630N + 250 \)