SOLUTION: Hi Bill and Ben had some sweets. After giving away 5/7 of his sweets, Bill had 2/3 as many sweets as Ben. After Ben gave 120 sweets away he now had 1/4 as much as Bill. How

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Question 1167914: Hi
Bill and Ben had some sweets. After giving away 5/7 of his sweets, Bill had 2/3 as many sweets as Ben. After Ben gave 120 sweets away he now had 1/4 as much as Bill.
How many sweets did each have at the start?
Thanks
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
Bill's sweets at start = x
Ben's sweets at start = y

2/7(x) = 2/3(y)
y - 120 = 1/4(2/7(x))

Simplify equations:

2/7(x) = 2/3(y)
y - 120 = 1/14(x)

2/7(x) - 2/3(y) = 0
-1/14(x) + y = 120

Multiply second equation by 2/3:

2/7(x) - 2/3(y) = 0
-1/21(x) + 2/3(y) = 80

Add both equations together:

5/21(x) = 80

Solve for x:

x = 80(21/5)

x = 336

Now that we know x = 336, we can plug this into any previous equation to find out what y equals.

2/7(x) = 2/3(y)

2/7(336) = 2/3(y)

96 = 2/3(y)

y = 96(3/2)

y = 144

Bill's sweets at start = x = 336
Ben's sweets at start = y = 144