David and Sam had an equal number of marbles. After Sam gave 50 marbles to David, he had 5x as many marbles as Sam. Find the total number of marbles they had.
David's marbles --- x
Sam's marbles -----x
After Sam lost his marbles:
Sam --- x-50
David -- x+50
x+50 = 5(x-50)
x+50 = 5x - 250
-4x = -300
x = 75
they had 75+75 or 150 marbles between them
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To solve this problem, we can use algebraic equations.
Let's assume that both David and Sam initially had the same number of marbles, which we'll represent as 'x'.
After Sam gave 50 marbles to David, Sam had 'x - 50' marbles and David had 'x + 50' marbles.
According to the given information, David had 5 times as many marbles as Sam after receiving the 50 marbles. So, we can write the equation:
x + 50 = 5(x - 50)
Now, let's solve this equation:
x + 50 = 5x - 250
250 + 50 = 5x - x
300 = 4x
x = 75
Therefore, both David and Sam initially had 75 marbles each.
To find the total number of marbles they had, we add the number of marbles they initially had:
Total number of marbles = 75 + 75 = 150
Hence, the total number of marbles they had together is 150.