Question

Suppose there are two brothers, Alex and Ben, who have saved up some money over the years. Alex saved $50 initially and decided to add $20 to his savings every month. Ben saved $80 initially and decided to add $15 to his savings every month. Both of them continue saving until they reach the same amount of money.

Write an equation representing Alex's savings after 'n' months.
Write an equation representing Ben's savings after 'n' months.
Determine the number of months it will take for Alex and Ben to have the same amount of money.
Note: In this problem, we're not looking for the value of 'n', but rather the expressions representing Alex's and Ben's savings after 'n' months.

Answer 1

Explanation:

A(n) = Alex's savings after n months = 20n + 50

B(n) = Ben's savings after n months = 15n + 80

to find the number of months until both have the same (!) amount of money saved we simply need to make both equations equal (find the n for which both are equal) :

20n + 50 = 15n + 80

5n + 50 = 80

5n = 30

n = 6

after 6 months they will have the same amount of money.