SOLUTION: The value of a certain 2 digit number is 5 times the sum of its digits. If the digits are reversed,the resulting number 9 more than the original number . Find the original number.

Question 68859: The value of a certain 2 digit number is 5 times the sum of its digits. If the digits are reversed,the resulting number 9 more than the original number . Find the original number. T is supposed to represent the tens, and U is supposed to represent the unit. Help. Need to write out this equation and solve it. Spent 3 hours already!!
Found 2 solutions by stanbon, rmromero:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The value of a certain 2 digit number is 5 times the sum of its digits. If the digits are reversed,the resulting number 9 more than the original number . Find the original number. T is supposed to represent the tens, and U is supposed to represent the unit.
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Value = 10T+U (Just like 32 = 10(3)+2)
5 times sum of its digits = 5(T+U)
If digits are reversed Value = 10U+T
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EQUATIONS:
1st: 10T+U=5(T+U)
2nd: 10U+T = 10T+U+9
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Rewrite the equations:
1st becomes: 5T-4U=0
2nd becomes: 9T-9U+9=0
2nd again: T-U=-1
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Rewriting the two equations:
1st: 5T-4U=0
2nd:T-U=-1
Solve 2nd for T to get:
3rd: T=U-1
Substitute into 1st to get:
5(U-1)-4U=0
U=1
Substitute that into 3rd to get:
T=1-1=0
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The two digit number is 01
When you reverse it you get 10 which is 9 more than the original.
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Cheers,
Stan H.

Answer by rmromero(383) (Show Source): You can put this solution on YOUR website!
What is asked in the problem?
Find the original number

Given:
The value of a certain 2 digit number is 5 times the sum of its digits
the number is reversed, the resulting number is 9 more than the original number.
Representation:
T = tens digit
U = unit digit

Write an Equation using the given sentence. since tens digit means t(10) and unit digit means u(1), 10t + u = the original two digit number.

The value of a certain 2 digit number is 5 times the sum of its digits
10t + u = 5(t+u)
Simplify the equation
10t + u = 5t + 5u
5t - 4u = 0

If the number is reversed u became the tens digit and t became the unit digit. u(10) for tens digit and t(1) for unit digit when the number is reversed. 10u + t = number is reversed
the number is reversed, the resulting number is 9 more than the original number.
10u + t = (10t + u) + 9
simplify the equation.
9u - 9t = 9
u - t = 1
Solve the variable using substitution method.

Here are the Steps using Substition method
1. In either equation, solve for one variable in terms of the other.
u - t = 1
u = t + 1
2. Substitute for that variable in the other equation. Solve.
5t - 4u = 0
5t - 4(t+1) = 0
5t - 4t -4 = 0
t = 4
3. Substitute the result from step 2 in either equation. Solve for the other variable.
u = t + 1 , t=4
u = 4 + 1
u = 5

4. Check the solution in both original equations.
5t - 4u = 0, t = 4 , u = 5
5(4) - 4(5) = 0
20 - 20 = 0
0 = 0 ----------> True

u - t = 1, t = 4 , u = 5
5 - 4 = 1
1 = 1 ---------->> True

Therefor the tens digit is 4 and the unit digit is 5
the original number now is 10t + u when t = 4 and u = 5
10(4) + 5 = 40 + 5 = 45

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