Dan has twice as many stickers as Cam does. If Dan gives Cam 15 of his stickers he will still have 22 more than Cam. How many stickers does each boy have?
To solve this problem, let's set up some equations.
Let's assume the number of stickers Cam has is "c".
According to the problem, Dan has twice as many stickers as Cam, so the number of stickers Dan has is "2c".
If Dan gives Cam 15 stickers, he will have 22 more than Cam. This means that after the transaction, Cam will have the same number of stickers as he had before, plus the 15 he received from Dan.
Now let's set up an equation to represent this information:
2c - 15 = c + 15 + 22
To simplify this equation, we can combine like terms:
2c - 15 = c + 37
Next, let's isolate the variable "c" by subtracting "c" from both sides:
2c - c - 15 = 37
Simplifying further:
c - 15 = 37
Now, let's isolate the variable "c" by adding 15 to both sides:
c = 37 + 15
Solving this equation:
c = 52
Therefore, Cam has 52 stickers.
Since Dan has twice as many stickers as Cam, he would have 2 times the amount:
2 * 52 = 104
Therefore, Dan has 104 stickers.
To summarize:
Cam has 52 stickers, and Dan has 104 stickers.
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D = 2C
D - 15 = C + 22
Substitute 2C for D in the second equation and solve for C. Insert that value into the first equation to solve for D. Check by putting both values into the second equation.
Initially:
Cam has X stickers.
Dan has 2x.
Dan gives Cam 15 stickers:
Cam has x + 15 stickers.
Dan has 2x - 15 stickers.
2x - 15 = (x + 15) + 22.
X = 52 stickers.
x + 15 = 52 + 15 = 67 stickers.
2x - 15 = 2*52 - 15 = 89 stickers.