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?

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): You can put this solution on YOUR website!

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) 3/10
(b) 60 candies

Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
c, how many candies total

Joseph,
Kenny, -------extremely obvious

Joseph took 24 more candies than Kenny.

----------the number of candies
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

let x be the number of candies in the bag originally.

Then (7/10)x is the number Joseph took.

Then Kenny took the rest, which is x - (7/10)x = (3/10)x.

Joseph took 24 more than Kenny:

(7/10)x = (3/10)x+24
(4/10)x = 24
x = (10/4)(24 = 10(6) = 60

ANSWERS:
(a) 3/10
(b) 60

RELATED QUESTIONS
A bag of candies was distributed equally among 16 pupils. When 7 of these pupils gave up... (answered by greenestamps)
Eight girls arrived at Lucy's party. During the party, Lucy passed around a jar of... (answered by Theo)
In a bag of candies there are 13 red candies, 13 green candies, 13 yellow candies, and 13 (answered by edjones)
A snack-size bag of M&Ms candies is opened. Inside, there are 12 red candies, 12 blue, 7... (answered by Boreal)
A snack-size bag of M&Ms candies is opened. Inside, there are 12 red candies, 12 blue, 7... (answered by ikleyn)
In a bag of candy, there are five red candies for every two green candies. If there are... (answered by stanbon)
There are 225 candies in a box. The candies are hershies, goya and munchers in terms of... (answered by ikleyn,MathTherapy)
a total of 42 candies are divided among some boys and girls. if boys receives 3/7 of the (answered by josgarithmetic)
I Got 2 Questions. 1.In a gym class, there are 12 boys and 18 girls. If the teacher... (answered by solver91311)