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Question 573775: One number is 8 more than another. If the sum of the smaller number and twice the larger number is 46, find the two numbers.
Answer by mathsmiles(68)   (Show Source):
You can put this solution on YOUR website! Let's use X and Y for the two numbers we're looking for. Let's also assume X is larger than Y. So X is 8 more than Y
X = Y + 8
The next part says to take the sum of the smaller number (Y) and twice the larger number (2X) giving 46.
Y + 2X = 46
That's enough info for us. Let's use substitution since we already have an equation with X by itself. So, substitute (Y+8) for all instances of X in the second equation:
Y + 2X = 46
Y + 2(Y+8) = 46 Multiplying out the paren:
Y + 2Y + 16 = 46 Combining like Y terms:
3Y + 16 = 46 subtracting 16 from each side:
3Y = 30 divide by 3 on each side:
Y = 10
But what's X? We know X is 8 more than Y from the original problem again.
If Y is 10, X is 10+8 = 18
Checking our answer using the 2nd formula:
Y + 2X = 46
(10) + 2(18) = 46
10 + 36 = 46
46 = 46 Correct!
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