Tina and Gopal had some stickers in the ratio 2:3. Gopal gave half of his stickers away and the ratio became 4:3. If Gopal had given away 21 stickers, how many stickers did each person have at first?
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whats the answer?
To solve this problem, let's first assign variables to the number of stickers Tina and Gopal had originally. Let's say Tina had 2x stickers and Gopal had 3x stickers.
According to the given information, when Gopal gave away half of his stickers, the new ratio became 4:3. This means that Tina now had 4 parts and Gopal had 3 parts. We can write this as:
Tina: 4x
Gopal: 3x
We also know that Gopal gave away 21 stickers, which was half of the original number of stickers he had. Since 3x represents the original number of stickers Gopal had, we can set up the following equation:
3x/2 = 21
To solve for x, we can multiply both sides of the equation by 2:
3x = 42
Dividing both sides by 3, we get:
x = 14
Now that we know the value of x, we can find the original number of stickers each person had:
Tina: 2x = 2 * 14 = 28 stickers
Gopal: 3x = 3 * 14 = 42 stickers
Therefore, Tina had 28 stickers and Gopal had 42 stickers originally.