SOLUTION: The sum of the digits of a two digit number is ten. The original number is two more than five times the units digit. Find this number.

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Question 715216: The sum of the digits of a two digit number is ten. The original number is two more than five times the units digit. Find this number.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
a = tens digit
b = units digit
The value of the number is 10a%2Bb

"The sum of the digits of a two digit number is ten" translates as
a%2Bb=10

"The original number is two more than five times the units digit" translates as
10a%2Bb=5%2Ab%2B2 --> 10a%2Bb=5b%2B2 --> 10a%2Bb-5b=5b%2B2-5b --> 10a-4b=2

We need to solve the system system%28a%2Bb=10%2C10a-4b=2%29
we can solve the first equation for a and substitute the expression found for a in the second equation to find b
a%2Bb=10 --> a=10-b
10a-4b=2 --> 10%2810-b%29-4b=2 --> 100-10b-4b=2 --> 100-14b=2 --> 100-14b%2B14b-2=2%2B14b-2 --> 100-2=14b --> 98=14b --> 98%2F14=14b%2F14 --> highlight%28b=7%29
Now we substitute that value into one of the equations to find a :
a%2Bb=10 --> a%2B7=10 --> a=10-7 --> highlight%28a=3%29
The number is highlight%2837%29