SOLUTION: The sum of the digits of a two digit number is 15. One third of the number diminished by 12 is 17. What is the number. Show your solution

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Question 1063388: The sum of the digits of a two digit number is 15. One third of the number diminished by 12 is 17. What is the number. Show your solution
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
t, TENS
u, ONES
system%28t%2Bu=15%2C%281%2F3%29%2810t%2Bu%29-12=17%29


%2810t%2Bu%29%2F3=29
10t%2Bu=3%2A29=87
u=87-10t
--
Digit sum equation t+u=15
t%2B87-10t=15
-9t=15-87
t=%2887-15%29%2F9
t=72%2F9
highlight%28t=8%29

Number is 87

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the tens digit = +t+
Let the units digit = +u+
--------------------------
(1) +t+%2B+u+=+15+
(2) +%281%2F3%29%2A%28+10t+%2B+u+%29+-+12+=+17+
-----------------------------------
(2) +%281%2F3%29%2A%28+10t+%2B+u+%29+=+29+
(2) +10t+%2B+u+=+87+
+t+=+8+
+u+=+7+
(1) +t+%2B+u+=+15+
(1) +8+%2B+7+=+15+
(1) +15+=+15+
OK
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The number is 87