# math

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2/3 of Ryan's stickers is equal to 3/4 of Tony's stickers. After Ryan gives 48 stickers to Tony, they have the same number of stickers. How many stickers does Ryan have at first?

• math -

Let x = number of Ryan's stickers
Let y = number of Tony's stickers
From the first statement,
(2/3)x = (3/4)y
From the second statement,
x - 48 = y + 48
Then we solve for x and y. There are many ways to solve this system, but let's do substitution.
To do substitution, we choose one equation and represent one of the variables in terms of the other. Then we substitute it to the other equation. Here, let's choose the variable x in the 2nd equation:
x - 48 = y + 48
x = y + 48 + 48
x = y + 96
Substitute it to the 1st equation:
(2/3)x = (3/4)y
(2/3)(y + 96) = (3/4)y
[(2/3)y + 64 = 3/4 y]*12
8y + 768 = 9y
8y - 9y = -768
-y = 768
y = 768 stickers (Tony's)
x = y + 96
x = 768 + 96
x = 864 stickers (Ryan's)

Hope this helps~ :)

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