SOLUTION: There were some candies in a bag. Joseph took 7/10 of the candies and Kenny took the rest. Joseph took 24 more candies than Kenny.
(a) What fraction of the candies did Kenny take?
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-> SOLUTION: There were some candies in a bag. Joseph took 7/10 of the candies and Kenny took the rest. Joseph took 24 more candies than Kenny.
(a) What fraction of the candies did Kenny take?
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Question 1204287: There were some candies in a bag. Joseph took 7/10 of the candies and Kenny took the rest. Joseph took 24 more candies than Kenny.
(a) What fraction of the candies did Kenny take?
(b) How many candies were there in the bag at first? Found 3 solutions by math_tutor2020, josgarithmetic, greenestamps:Answer by math_tutor2020(3817) (Show Source):
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k = amount of candies that Kenny took
k+24 = amount of candies that Joseph took
k is a positive integer
k+(k+24) = 2k+24 = total amount of candies
Joseph took 7/10 of this total.
This must mean Kenny took 3/10 of the candies because
1 - (7/10) = 3/10
Think of a pizza with 10 slices. Joseph gets 7 slices and Kenny takes the remaining 3 slices.
(7/10)*total = amount Joseph took
(7/10)*(2k+24) = k+24
7(2k+24) = 10(k+24)
14k+168 = 10k+240
14k-10k = 240-168
4k = 72
k = 72/4
k = 18
Or we could have these steps
(3/10)*total = amount Kenny took
(3/10)*(2k+24) = k
3(2k+24) = 10k
6k+72 = 10k
72 = 10k-6k
72 = 4k
4k = 72
k = 72/4
k = 18
Either way, Kenny took 18 candies.
k+24 = 18+24 = 42
Joseph took 42 candies.
In total there are 18+42 = 60 candies to start off.
7/10 of this is (7/10)*60 = 0.7*60 = 42 to represent how much Joseph took. We have confirmed the answers are correct.
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