AbeNeedsAnswers wrote:If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?
A) 3
B) 6
C) 7
D) 8
E) 10
RULE:
(multiple of k) ± (multiple of k) = multiple of k.
Since y is a multiple of 5, let y=5a.
Substituting y=5a into 3x + 4y = 200, we get:
3x + 4(5a) = 200.
3x + 20a = 200
3x = 200 - 20a.
3x = (multiple of 20) - (multiple of 20).
In accordance with the rule above:
(multiple of 20) - (multiple of 20) = multiple of 20.
Thus:
3x = multiple of 20.
For 3x to be a multiple of 20, x must be a multiple of 20.
Thus, x must also be a multiple of 10.
The correct answer is
E.
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