Two runners are saving money to attend a marathon. The first runner has $112 in savings, received a $45 gift from a friend, and will save $25 each month. The second runner has $50 in savings and will save $60 each month. Which equation can be used to find m, the number of months it will take for both accounts to have the same amount of money?

Question

darkknight · Answer

let the first runner be f and the second runner be known as g
so f(x) is 112 (from the amount in f's savings) + 45 (his gift) + 25x (for he will save 25 each month)
simplify all of that into 25x+157
so for g(x) he has 50 (from savings) and gets 60x (60 per month)
so simplify into g(x) = 60x+50. 
To find when they have the same amount stored at the same time set the eqn's equal to each other. 
25x+157 = 60x+50
solve for x