SOLUTION: A number between 20 and 30 and is three times the sum of its digits. What is the number? How do you work this problem

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Question 1111392: A number between 20 and 30 and is three times the sum of its digits. What is the number?
How do you work this problem
Found 2 solutions by mananth, greenestamps:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
A number between 20 and 30 and is three times the sum of its digits. What is the number?
Let the number be 10x+y
but x=2
the number is 20+y
(20+y) = 3(2+y)
20+y = 6+3y
2y=14
y=7
the number is 27
check
27= 3(2+7)

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


Algebraically, if x is the units digit, then the number is 20+x and the sum of its digits is 2+x. So

20%2Bx+=+3%282%2Bx%29
20%2Bx+=+6%2B3x
14+=+2x
x+=+7

The units digit is 7; the number is 27.

Using algebra to solve this problem is good practice with algebra; but the problem is easily solved with a little mental arithmetic.

The number is 3 times the sum of its digits, so it is a multiple of 3.

The only multiples of 3 between 20 and 30 are 21, 24, and 27.

Only 27 satisfies the condition that it is 3 times the sum of its digits.