SOLUTION: The sum of two numbers is eighteen. The total of three times the smaller and twice the larger is forty-four. Find the two numbers.

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Question 1154744: The sum of two numbers is eighteen. The total of three times the smaller and twice the larger is forty-four. Find the two numbers.
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let the two numbers be x (larger number) and y (smaller number)
if the sum of two numbers is eighteen, we have
x%2By=18........solve for x
x=18-y......... eq.1

if the total of three+times the smaller and twice the larger is forty-four, we have

2x%2B3y=44........eq.2.....substitute x from eq.1
2%2818-y%29%2B3y=44....solve for y
36-2y%2B3y=44
y=44-36
y=8
go to
x=18-y......... eq.1,substitute y
x=18-8
x=10

the two numbers are 10 and 8


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


If a formal algebraic solution is not required, you can get some good mental exercise solving this informally.

The sum of the two numbers is 18.

Double that: the sum of twice the smaller and twice the larger is 36.

We are given that the sum of THREE times the smaller and twice the larger is 44.

Therefore (comparing the last two sentences) the smaller number is 8.

And therefore the larger number is 10.