SOLUTION: Two numbers differ by 16. The sum of twice the larger number and three times the smaller number is equal to 72. Find the numbers

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Question 699427: Two numbers differ by 16. The sum of twice the larger number and three times the smaller number is equal to 72. Find the numbers
Answer by neatmath(302) About Me  (Show Source):
You can put this solution on YOUR website!

This is a system of equations with two variables:

Let x be the larger number, let y be the smaller number. Then:

x-y=16 given

%282%2Ax%29%2B%283%2Ay%29=72 given

At this point you can use any method to solve for x or y.

Let's use substitution, by solving the first equation for x:

x=y%2B16

Then substitute this value for x into the second equation:

%282%2A%28y%2B16%29%29%2B%283%2Ay%29=72

2y%2B32%2B3y=72

5y%2B32=72

5y=40

y=8

If y=8, then it is easy to see that:

x-y=16

x-8=16

x=24

So the two numbers are 24 and 8.

Check it, it works.

I hope this helps! Keep practicing! :)

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