James had $240 more than his
brother, Sam, at first. After their mother gave James $30 and Sam $50 James had twice as much money as Sam. How much money
did Sam have at first?
Let's work through the problem step by step:
1. Let's assume that Sam had x dollars at first.
2. We are told that James had $240 more than Sam initially, so James would have had (x+240) dollars.
3. After their mother gave James $30, James would have (x+240+30) dollars.
4. After their mother gave Sam $50, Sam would have (x+50) dollars.
5. We are also given that after receiving their respective amounts from their mother, James had twice as much money as Sam. So we can write the equation: (x+240+30) = 2(x+50).
6. Expanding the equation gives: x+270 = 2x+100.
7. Subtracting x from both sides gives: 270 = x+100.
8. Subtracting 100 from both sides gives: x = 170.
So, Sam had $170 at first.
To find out how much money Sam had at first, we can solve this problem by setting up equations based on the given information. Let's assume that Sam had x dollars at the beginning.
We are given that James had $240 more than Sam at first. So, James had (x + $240) dollars.
After their mother gave James $30 and Sam $50, their new amounts became (x + $240 + $30) and (x + $50) dollars, respectively.
We are also given that after their mother gave them the money, James had twice as much money as Sam. Mathematically, this can be written as:
x + $240 + $30 = 2(x + $50)
Let's simplify and solve this equation:
x + $270 = 2x + $100
Combining like terms, we get:
x - 2x = $100 - $270
-Sx = -$170
Dividing both sides by -1 gives:
x = $170
Therefore, Sam had $170 at the beginning.
At first:
Sam had ---- x
James had --- x+240
after mother's charity:
Sam had x + 50
James had x+240 + 30 = x + 270
x + 270 = 2(x+50)
x + 270 = 2x + 100
-x = -170
x = 170
Sam had $170 and James had 410
check:
after mom: Sam had 170+50 = 220
james had 410 + 30 = 440 , which is twice what Sam had