Question

Bill has 4 times as much money as Ted. If Ted spends $100 and Ted spends 75, Bill will have 5 times as much money as ted. How much money do Bill and Ted have?

Answer 1

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