Posted by **Anonymous** on Thursday, February 28, 2013 at 9:50pm.

The sum of the digits of a certain two-digit number is 7. Reversing its digits increase the number by 9. What is the number. Use x and y. Please help me!!!!

- algebra -
**Reiny**, Thursday, February 28, 2013 at 10:54pm
in the original number, let the unit digit be x, then tens digiti be y

so the original number is 10y + x

where x+y = 7

the number reversed will be 10x + y

new number - old number = 9

10x + y - (10y + x) = 9

9x - 9y = 9

or x-y = 1

x+y=7

x-y=1

add them

2x = 8

x = 4, then y = 3

the number is 10y+x = 34

check:

original number is 34

reversed number is 43

is the number increased by 9 ??? YES

is the sum of the digits 7 ??? YES

YEAHHH

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