You and your friend are saving for a vacation. You start with the same amount and save for the same

You and your friend are saving for a vacation. You start with the same amount and save for the same number of weeks. You save 75 per week, and your friend saves 50 per week. When vacation time comes, you have 950, and your friend has 800. How much did you start with, and for how many weeks did you save?

Let w be the number of weeks. Set up two equations where s is the starting amount:
(1) s + 75w =950
(2) s + 50w = 800

Rearrange (1) into (3) to solve for s by subtracting 75w
(3) s = 950 - 75w

Rearrange (2) into (4) to solve for s by subtracting 50w
(4) s = 800 - 50w

Set (3) and (4) equal to each other so solve for w
950 - 75w = 800 - 50w

Add 75w to each side, and subtract 950 from each side:
25w = 150

Divide each side by w
w = 6

Now plug w = 6 into (3)
s = 950 - 75(6)
s = 950 - 450
s = 500