Posted by **Joe Mhar Plaza** on Thursday, January 6, 2011 at 10:34pm.

The sum of the of a two-digit number is 15. One third of the number diminished by 12 is 17. Find the number.

- Exploring mathematics elementary algebra -
**Reiny**, Thursday, January 6, 2011 at 10:52pm
Did you mean the "sum of the digits of a two-digit number is 15" ?

if so, then

let the unit digit be x

let the tens digit be y

so the value is 10y + x

"One third of the number diminished by 12 is 17"

---> (1/3)(10y+x) - 12 = 17

(1/3)(10y+x) = 29

multiply by 3

10y+x = 87

x = 87 - 10y

also x+y = 15

by substitution:

87-10y + y = 15

-9y = -72

y = 8

x = 87 - 80 = 7

the number is 87

check the properties stated.

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