David and John shared some money in the ratio 5:2 John received $30 less than David. How much money did John get?
Represent the unknowns. Since the ratio of their money shared is 5 (David) : 2(John),
Let 5x = David's money
Let 2x = John's money
In the problem, John received $30 less than David. Thus,
2x = 5x - 30
Solving,
2x - 5x = -30
-3x = -30
x = 10
Thus,
5x = $50 (David)
2x = $20 (John)
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To find out how much money John got, we need to understand the given information.
We know that the money was shared in a ratio of 5:2 between David and John. Let's assume that David received 5x dollars, where x is a constant. Similarly, John received 2x dollars.
According to the information given, John received $30 less than David. So we can create the equation 5x - 2x = 30.
Simplifying this equation, we have 3x = 30. By dividing both sides by 3, we find that x = 10.
Now that we know the value of x, we can substitute it into either David's or John's share to find the value of their money. Let's use John's share, which is 2x.
Substituting x = 10, we find that 2x = 2 * 10 = 20.
Therefore, John received $20.