algebra question

Question

Keith and Ranz had the same amount of money. Keith spent P250.00 while Ranz spent P510.00. After spending, Keith had three times as much as Ranz. How much money did Keith had three times as much as Ranz. How much money did Keith have at first?

Answer 1

The money Keith and Ranz originally had is "k" and "r" respectively.

The money they have after spending is k - 250 and r - 510.

After the spending occurred Keith has 3 times what Ranz has, which is k - 250 = 3(r -510), but since Keith and Ranz started with the same amount k = r and as can re-write this as k - 250 = 3(k -510) and solve:

k - 250 = 3(k -510) | distribute parenthesis

k - 250 = 3k - 1530 | + 1530

k + 1280 = 3k | - k

1280 = 2k | / 2

640 = k

Therefore r = 640 as well.

Verify...

640 - 250 = 3(640 -510) | solve parenthesis)

640 - 250 = 3(130)

640 - 250 = 390

390 = 390

Checks!

Answer 2

x=money they had at the very beginning

y=Amount of money Ranz had at the end

The following equations represent the flow of money for each person

Keith: 3y=x-250.00

Ranz: y=x-510.00

You can substitute the y in Ranz's equation for the y in Keith's equation.

3(x-510.00)=x-250.00

3x-1530.00=x-250.00

2x=1280.00

x=P640.00

Check

y=640.00-510.00=130.00

3(130.00)=640.00-250.00

390.00=390.00

Answer 3

Let k = the amount of money Keith had at first (equal for both)

k - 250 = 3(k - 510)

k - 250 = 3k - 1530

-2k = -1280

k = $640

Let's check.

640 - 250 = 390

640 - 510 = 130

3(130) = 390

390 = 390

0 = 0

Check!