Sharon, tracy and Rachel collected a total of 283 stickers. At first, sharon had 1/8 as many stickers as Tracy. When rachel gave 25 of her stickers to sharon, sharon had 1/4 as many stickers as tracy. How many stickers did rachel collect at first?
1unit= 25
2+8=10
10units= 25×10
= 250
283 - 250= 33 (Rachel after giving Sharon)
33 + 25 = 58 (Rachel had at first)
To solve this problem, we'll work through it step by step.
Let's assume the number of stickers Tracy has be x.
According to the given information, Sharon initially had 1/8 as many stickers as Tracy, so Sharon had (1/8)*x stickers.
The total number of stickers collected by Sharon, Tracy, and Rachel is 283, so we can form an equation:
Sharon's stickers + Tracy's stickers + Rachel's stickers = Total number of stickers
(1/8)*x + x + Rachel's stickers = 283
Next, we are given that when Rachel gave 25 stickers to Sharon, Sharon then had 1/4 as many stickers as Tracy. So, according to this new information, we have:
(1/4)*x = (1/8)*x + 25
Now we can solve these two equations simultaneously to find the value of x and then determine Rachel's initial number of stickers.
Let's solve the first equation:
(1/8)*x + x + Rachel's stickers = 283
Combining the x terms, we get:
(9/8)*x + Rachel's stickers = 283
Subtracting (9/8)*x from both sides, we get:
Rachel's stickers = 283 - (9/8)*x
Now, substitute this into the second equation:
(1/4)*x = (1/8)*x + 25
Multiply both sides by 8 to eliminate the fractions:
2x = x + 200
Subtracting x from both sides, we get:
x = 200
Now we can substitute x = 200 into the first equation to find Rachel's stickers:
Rachel's stickers = 283 - (9/8)*200
Rachel's stickers = 283 - 225
Rachel's stickers = 58
Therefore, Rachel collected 58 stickers initially.