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Question 1201374: Stickers were sold only in big sheets of 60 stickers each and small sheets of 25 stickers each. Andy and Ben bought the same number of sheets of stickers. Andy and Ben each bought some big sheets of stickers. Andy bought 8 small sheets of stickers and Ben bought 17 small sheets of stickers.
(a) What was the difference in the total number of stickers between Andy and Ben?
(b) Ben gave away all the big sheets of stickers that he had bought. As a result, he had 735 fewer stickers than Andy. How many sheets of stickers did each boy buy?
Found 3 solutions by ikleyn, math_tutor2020, greenestamps:
Answer by ikleyn(52802)   (Show Source):
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
Part (a)
Stickers were sold only in big sheets of 60 stickers each and small sheets of 25 stickers each. Andy and Ben bought the same number of sheets of stickers. Andy and Ben each bought some big sheets of stickers. Andy bought 8 small sheets of stickers and Ben bought 17 small sheets of stickers.
(a) What was the difference in the total number of stickers between Andy and Ben?
A = number of big sheets Andy bought
B = number of big sheets Ben bought
8 = number of small sheets Andy bought
17 = number of small sheets Ben bought
A+8 = total number of sheets Andy bought
B+17 = total number of sheets Ben bought
A+8 = B+17 since the two men bought the same number of sheets of stickers.
Isolate the variable A.
A+8 = B+17
A+8-8 = B+17-8
A = B+9
This says that Andy bought 9 more large sheets compared to Ben.
Large stickers
Andy = A large sheets = 60A = 60(B+9) = 60B+540 stickers
Ben = B large sheets = 60B stickers
Small stickers
Andy = 8 small = 8*25 = 200 stickers
Ben = 17 small = 17*25 = 425 stickers
Total stickers
Andy = large + small = (60B+540)+200 = 60B+740
Ben = large + small = 60B+425
Difference:
Andy - Ben = (60B+740)-(60B+425)
Andy - Ben = 60B+740-60B-425
Andy - Ben = (60B-60B)+(740-425)
Andy - Ben = 315
Answer: 315
Andy has 315 more stickers compared to Ben.
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Part (b)
Stickers were sold only in big sheets of 60 stickers each and small sheets of 25 stickers each. Andy and Ben bought the same number of sheets of stickers. Andy and Ben each bought some big sheets of stickers. Andy bought 8 small sheets of stickers and Ben bought 17 small sheets of stickers.
(b) Ben gave away all the big sheets of stickers that he had bought. As a result, he had 735 fewer stickers than Andy. How many sheets of stickers did each boy buy?
Ben's total = 60B+425, calculated in part (a)
Ben gave away all of his big sheets.
Ben's total is now 425 because the 60B represented the stickers from the large sheet.
Andy's total goes from 60B+740 to (60B+740)+60B = 120B+740 after getting the new set of stickers from Ben.
At this point Ben has 735 fewer stickers compared to Andy
Andy - Ben = 735
(120B+740) - (425) = 735
120B+315 = 735
120B = 735-315
120B = 420
B = 420/120
B = 3.5
Since B is not a whole number, I'll assume Ben didn't give Andy the big sheets of stickers. Rather I'll assume Ben gave them to someone else.
Andy's count = 60B+740
Ben's count = 425
Andy - Ben = 735
(60B+740) - (425) = 735
60B+315 = 735
60B = 735-315
60B = 420
B = 420/60
B = 7
We get a whole number here, so this seems to fit much better.
Ben bought 7 large sheets + 17 small sheets = 24 sheets total.
Andy bought 16 large sheets + 8 small sheets = 24 sheets total.
note that 16 = 7+9, showing Andy bought 9 more large sheets compared to Ben.
Answer: 24 sheets for each person.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
(a) Each boy bought the same number of sheets of stickers. Ben bought 17-8 = 9 more small sheets than Andy. The difference between the number of stickers on a large sheet and a small sheet is 60-25 = 35. So Ben has 9*35 = 315 stickers fewer than Andy.
ANSWER: 315
(b) Before Ben gave away all his large sheets, he had 315 stickers fewer than Andy; afterwards, he had 735 fewer. So the large sheets he gave away had a total of 735-315 = 420 stickers. Since each large sheet has 60 stickers, the number of sheets of large stickers he gave away was 420/60 = 7.
Then, since Ben bought 17 small sheets of stickers, the total number of sheets he bought was 7+17 = 24.
And we know both boys bought the same number of sheets of stickers, so....
ANSWER: Each boy bought 24 sheets of stickers
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