SOLUTION: could show me how to work this problem please If we multiply the sum of numbers of a 2 digit number by 3, add 10 to the product, divide the outcome by 2, and subtract 11 from the q

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Question 699607: could show me how to work this problem please If we multiply the sum of numbers of a 2 digit number by 3, add 10 to the product, divide the outcome by 2, and subtract 11 from the quotient, we get the original number. Find this two digit number.
please
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A two digit number, where:
a = the 10's digit
b = the units
then
10a+b = the two digit number
:
" If we multiply the sum of numbers of a 2 digit number by 3, add 10 to the product, divide the outcome by 2, and subtract 11 from the quotient, we get the original number."
%283%28a%2Bb%29+%2B+10%29%2F2 - 11 = 10a+b
Multiply by 2 to get rid of the denominator
3(a+b) + 10 - 2(11) = 2(10a+b)
:
3a + 3b + 10 - 22 = 20a + 2b
3a + 3b - 12 = 20a + 2b
3b - 2b = 20a - 3a + 12
b = 17a + 12
the only single digit integer for b occurs when a = -1, then b = -5
:
Find this two digit number. -15 is the original number
:
:
Check this in the original equation
%283%28-1-5%29+%2B+10%29%2F2 - 11 = 10(-1) - 5
%283%28-6%29%2B10%29%2F2 - 11 = -15
%28-18%2B10%29%2F2 - 11 = -15
-4 - 11 = -15