Question 1204287
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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.



Answers:
(a) <font color=red size=4>3/10</font>
(b) <font color=red size=4>60 candies</font>
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