David and Peter had $90 and $200 respectively. They were each given an equal amount of money. Then Peter had twice as much money as David. How much money did each boy receive?
I think it should be calculated like this:
Let x be the amount of money each boy received
2*(90+x)=200+x or 90+x=(200+x)/2
180+2x=200+x
x=20
Therefore, each boy received $20
Let's assume that each boy received an equal amount of money, let's call it 'x'.
Initially, David had $90 and Peter had $200.
After receiving the equal amount of money 'x', David would have $90 + x.
After receiving the equal amount of money 'x', Peter would have $200 + x.
According to the given information, Peter then had twice as much money as David.
So, we can write the equation: 2 * (David's money after receiving x) = Peter's money after receiving x.
2 * (90 + x) = 200 + x
Expanding the left side of the equation, we get: 180 + 2x = 200 + x
Now, let's solve for x.
Subtracting 'x' from both sides of the equation, we get: 180 + x = 200
Subtracting 180 from both sides of the equation, we get: x = 20
Therefore, each boy received $20.
So, David received $20 and Peter also received $20.
To solve this problem, we need to set up an algebraic equation based on the given information.
Let's assume David and Peter each received x dollars. After receiving this amount, David has a total of $90 + x, and Peter has a total of $200 + x.
According to the problem, Peter's total is twice as much as David's total. Translating that into an equation, we have:
$200 + x = 2($90 + x)
To solve this equation, we will distribute the 2 to both terms inside the parentheses:
$200 + x = $180 + 2x
Next, we will rearrange the equation to isolate the variable on one side:
x - 2x = $180 - $200
Simplifying both sides of the equation, we get:
-x = -$20
We can now solve for x by dividing both sides of the equation by -1:
x = $20
Therefore, each boy received $20.