SOLUTION: the sum of the two-digit number is 11. When the number is reversed, the number is 63 less than the original number. Find the original number and show work.

Question 72232: the sum of the two-digit number is 11. When the number is reversed, the number is 63 less than the original number. Find the original number and show work.
Found 2 solutions by stanbon, rmromero:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
the sum of the two-digit number is 11. When the number is reversed, the number is 63 less than the original number. Find the original number and show work.
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Let the two digit number be tu: t is the ten's digit; u is the unit's digit
The value of this number is 10t+u just like 23 is worth 10*2+3
The value of its reverse is 10u+t
--------
EQUATION:
t+u=11
10u+t+63=10t+u
-------------------
Rewrite as:
t+u=11
9t-9u=63
---------------
Rewrite Again:
t+u=11
t-u=7
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Add the two equations to get:
2t=18
t=9
-------
Solve for u:
9+u=11
u=2
--------
The original number is 92
The number reversed is 29
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Cheers,
Stan H.

Answer by rmromero(383) (Show Source): You can put this solution on YOUR website!

the sum of the two-digit number is 11. When the number is reversed, the number is 63 less than the original number. Find the original number and show work.
What is asked in the problem?
Find the original number
Given:
The sum of the two-digit number is 11
When the number is reversed, the number is 63 less than the original number
Representation:
Let t = tens digit
u = unit digit
10t + u = the original two-digit number
10u + t = the reversed two-digit number
Equation:Translate the given sentences to mathematical sentences
t + u = 11
10u + t = (10t + u) - 63 Simplify
9u - 9t = -63 Divide both sides by 9
u - t = -7

Solve the two equation simultaneously by elimination or substitution.
I will use elimination method
t + u = 11
-t + u = -7
____________
2u = 4 divide 2 both sides
u = 2
Substitute u = 2, to any of the two equations to find the other variable t.
t + u = 11, u = 2
t + 2 = 11
t = 11 - 2
t = 9
To find the original number, substitute t = 9 and u = 2
10t + u = 10(9) + 2
= 90 + 2
= 92 -------------->> answer

If you want to check substitute t = 9 and u = 2 to any of the two equations
then if the two equation are true after substituting, then you're answer
is correct.
Happy calculating

Rachel

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