Stephanie had 24 more stickers than Jolene. Stephanie gave half of her stickers to Jolene. Jolene in return gave half of what she had to Stephanie. In the end, Stephanie had 40 more stickers than Jolene. How many stickers did Stephanie have in the end?
at the start:
Joline ---- x stickers
Steph ----- x+24
Steph gave 1/2 of hers to Joline
Joline now has ---- x + (x+24)/2= (3x+24)/2
Step now has --- (x+24)/2
now joline give half of what she has to Steph
Joline now has ---- (3x+24)/4
Steph now has ---- (x+24)/2 + (3x+24)/4 = (5x+72)/4
now Step has 40 more than Joline
(5x+72)/4 = (3x+24)/4+ 40
times 4
5x + 72 = 3x + 24 + 160
2x = 112
x = 56
at the end Steph has (5x+72)/4 or (5(56)+72)/4 or 88 stickers
let's check this:
at the start:
Joline had x or 56 stickers
Steph had x+24 or 80
steph gave half of hers or 40 to Joline, so
Joline now has 96
Steph has 40
finally joline gives half or 48 to steph
so Joline has 48 and
Steph has 40+48 = 88
YEAHHH
THANKS FOR U R HELP
To solve this problem, let's break it down step by step.
1. Let's assume that Jolene had x stickers initially.
2. According to the problem, Stephanie had 24 more stickers than Jolene, so Stephanie had x + 24 stickers initially.
3. Stephanie gave half of her stickers to Jolene, which means Stephanie gave (x + 24) / 2 stickers to Jolene. Therefore, Stephanie has (x + 24) / 2 stickers left.
4. Jolene, in return, gave half of what she had to Stephanie, which means Jolene gave x / 2 stickers to Stephanie. Consequently, Jolene has x / 2 stickers left.
5. In the end, Stephanie had 40 more stickers than Jolene, which means (x + 24) / 2 = (x / 2) + 40.
6. Now, let's solve the equation:
- Distributing the division: x/2 + 12 = x/2 + 40
- Simplifying the equation: x/2 - x/2 = 40 - 12
- Combining like terms: 0x/2 = 28
- Simplifying the left side: 0 = 28
This equation is contradictory and doesn't have a solution. Hence, there is no possible number of stickers that satisfies the conditions given in the problem.