Linear eqns: A number consists of two digits which add up to

1+1=2

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Nov 20, 2006
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A number consists of two digits which add up to 9. When the digits are reversed, the original number is decreased by 45. What is the original number?

So here's what I've done:

10A + B = C
A + 10B = C - 45

-10(10A + B = C)

A + 10B = C - 45
-100A - 10B = -10C

so i get

99A = 9C - 45

11A = 1C - 5

After this step I have been trying all different ways but getting no where. Do you have to make a second elimination equation with now only C and B or something? Please can some one help me finish this one up or/and point out any misstakes I've made.
 
you're using too many variables.

let A = tens digit of the original number
B = units digit of the original number

original number = 10A + B

When the digits are reversed, the original number is decreased by 45.

10B + A = 10A + B - 45

since A + B = 9, B = 9 - A ...

10(9 - A) + A = 10A + (9 - A) - 45

now, solve for A, then remember that B = 9 - A.

you should get the original number to be 72.
 
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