# algebra

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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 -

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
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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