SOLUTION: This one boggles my mind! One number is 2 less than another. If 9 times the smaller number minus 2 times the larger number is 52, find the two numbers.

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Question 106801: This one boggles my mind!
One number is 2 less than another. If 9 times the smaller number minus 2 times the larger number is 52, find the two numbers.

Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Let's see if we can unboggle your mind.
Let the smaller number be x and the larger number be y.
x = y-2 "One number is 2 less than another number"
9x-2y = 52 "...9 times the smaller number minus 2 times the larger number is 52"
Substitute the x = y-2 into the second equation and solve for y.
9(y-2)-2y = 52 Simplify.
9y-18-2y = 52
7y-18 = 52 Add 18 to both sides.
7y = 70 Divide both sides by 7.
y = 10 ...and
x = y-2
x = 10-2
x = 8
The two numbers are: 8 and 10
Check:
x = y-2
8 = 10-2
8 = 8
9x-2y = 52
9(8)-2(10) = 52
72 - 20 = 52
52 = 52