Question:
Bill has four times as much money as Ted. If Ted spends $100 and Bill spends $75, Bill will have five times as much money as Ted. How much money do Bill and Ted have before and after spending money?
Answer:
Before spending money, Bill has $1700 and Ted has $425
After spending money, Bill has $ 1625 and Ted has $ 325
Solution:
Let the amount of money Bill has be "b"
Let the amount of money Ted has be "t"
Bill has 4 times as much money as Ted, we can say the following:
b = 4t ---------- eqn 1
If Ted spends $100 and Ted spends 75, Bill will have 5 times as much money as ted.
b - 75 = 5 ( t - 100 ) ----- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 1 in eqn 2
4t - 75 = 5( t - 100 )
4t - 75 = 5t - 500
5t - 4t = 500 - 75
t = 425
From eqn 1,
b = 4(425) = 1700
b = 1700
So, before spending money, Bill has $1700 and Ted has $425.
After spending money:
Bill = b - 75 = 1700 - 75 = $ 1625
Ted = t - 100 = 425 - 100 = $ 325