SOLUTION: A two digit number whose ten digit is 2 more than the units digit is 3 more than 6 times the sum of its digits. Find the original number

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Question 1106095: A two digit number whose ten digit is 2 more than the units digit is 3 more than 6 times the sum of its digits. Find the original number
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


(1) Let the units digit be x; then the tens digit is x+2.

(2) The value of the number is 10(x+2)+x = 11x+20.

(3) 3 more than 6 times the sum of the digits is 6((x+2)+x)+3 = 12x+15.

The problem tells us that the expressions in (2) and (3) are equal:
11x%2B20+=+12x%2B15
5+=+x

The units digit is 5; the tens digit is 7.

CHECK: 6(5+7)+3 = 75

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
t, tens digit
u, units digit
system%28t=u%2B2%2C10t%2Bu=6%28t%2Bu%29%2B3%29

10t%2Bu=6t%2B6u%2B3
4t=5u%2B3
4%28u%2B2%29=5u%2B3
4u%2B8=5u%2B3
highlight%285=u%29
-
t=u%2B2
t=5%2B2
highlight%28t=7%29

The number is 75.