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Question 1078534: The sum of two numbers is fifty-three. The sum of 3 times the small and 4 times the larger is one hundred sixty-three. Find the two numbers.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! x+y=53 and they are the two numbers
3x+4y=163,
-3x-3y=-159, multiplying top by -3
y=4 by adding the two
x=49
check in the second equation
147+4*4=163, checks.
alternative
x+(53-x)=53
3x+4(53-x)=163
4x+212-4x=163
-x=-49
x=49
y=4
It isn't necessary to know which number is smaller. It is 3 times one of them and 4 times the other. If the larger one were multiplied by 3 and the smaller by 4, it wouldn't work
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