SOLUTION: One number is nine more than twice another. If their sum is decreased by ten, the result is eleven. Find the numbers.

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Question 1114249: One number is nine more than twice another. If their sum is decreased by ten, the result is eleven. Find the numbers.
Found 3 solutions by mananth, greenestamps, josgarithmetic:
Answer by mananth(16946)   (Show Source):
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lET THE NUMBERS BE X & Y
X=2Y +9
X-2Y=9
X+Y-10=11
X+Y=21
X-2Y=9
X+Y=21
SUBTRACT THE EQUATIONS
-3Y=-12
Y=4
X=2Y+9
X=2*4+9
X=17
17 AND 4

Answer by greenestamps(13200)   (Show Source):
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Knowing how to solve the problem using formal algebra, as shown by the other tutor, is useful. However, solving the problem by logical reasoning is excellent exercise for the brain.

(1) The sum is 11 after decreasing it by 10. So add the 10 back on; the sum of the two numbers is 21.

(2) The sum of the two numbers is 21, and one is 9 more than twice the other. Subtract that "extra" 9; now the sum of the two numbers is 12, and one of them is twice the other.

(3) If the sum of the two numbers is 12 and one is twice the other, the numbers are 4 and 8.

(4) Now add back on the 9 that you took away from the larger number. The original numbers are 4 and 8+9=17.

Answer by josgarithmetic(39617)   (Show Source):
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Numbers x and 2x+9
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and