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

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) (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
RELATED QUESTIONS
Hi Gary and Dave had some sweets. After Gary gave 5/7 of his sweets he had 2/3 as many... (answered by josgarithmetic,ikleyn)

Hi Ken and Ivan had some sweets. After ken gave away 5/7 of his sweets, he had 2/3 as... (answered by josgarithmetic,MathTherapy,advanced_Learner)

The ratios of the number of sweets Abigail has to the number of sweets Ben has is 4 : 5... (answered by jorel1380)

Hi Mandy and jack had some sweets in the ratio of 5:7.after mandy gave jack some sweets... (answered by ankor@dixie-net.com)

Clifford had 80% fewer sweets than Ashwin. After Ashwin gave 210 sweets to Clifford,... (answered by josgarithmetic)

Alex, Bernard and Cindy had a total of 840 sweets. The ratio of the number of sweets... (answered by ikleyn)

Edi bought some sweets. On Thursday, he gave some sweets to his friends. The number of... (answered by Edwin McCravy,greenestamps)

Hi ben and tom had a total of 144 sweets.ben gave tom 1/5 of what he had. Tom the gave... (answered by josgarithmetic,greenestamps)

Andy, Bernard and Cassandra shared a number of sweets in the ratio 3:7:5. Andy gave... (answered by greenestamps)