Daniel gave 4/5 of his stickers to Javier. Javier’s collection of stickers increased to 64. If Javier had 28 stickers in the beginning, how many stickers did Daniel have in the beginning?
so 4/5 of Daniel's stickers = 64
1/5 of Daniel's stickers = 16
5/5 of Daniel's stickers = 80
Let's assume Daniel had x stickers in the beginning.
Daniel gave 4/5 of his stickers to Javier, which means he gave away (4/5)x stickers.
After receiving stickers from Daniel, Javier's collection increased to 64, so we can write the equation:
28 + (4/5)x = 64
To solve for x, we can start by subtracting 28 from both sides of the equation:
(4/5)x = 64 - 28
Simplifying the equation further:
(4/5)x = 36
To isolate x, we multiply both sides by the reciprocal of 4/5, which is 5/4:
[(4/5)x] * (5/4) = 36 * (5/4)
Simplifying the equation:
Canceling out the common factors on both sides:
x = 45
Therefore, Daniel had 45 stickers in the beginning.
To solve this problem, we can use a proportion. Let's assume that Daniel had x stickers in the beginning.
According to the information given, Javier started with 28 stickers and after receiving 4/5 of Daniel's stickers, his collection increased to 64 stickers.
We can set up a proportion:
(x - 4/5x) / 28 = (64 - 28) / 28
Simplifying the equation, we get:
(1/5x) / 28 = 36 / 28
Now, cross-multiply:
(1/5x) * 28 = 36
Multiply both sides by 5:
28x = 180
Divide both sides by 28:
x = 180 / 28
Simplifying, we get:
x ≈ 6.43
Therefore, Daniel had approximately 6.43 stickers in the beginning. Since we cannot have a fraction of a sticker, we can say that Daniel had 6 stickers in the beginning.