SOLUTION: find a two digit number such that the number itself minus the sum of its digits equal 36.. The sum of the digits plus product of the digits equals the number minus eight.

Question 611097: find a two digit number such that the number itself minus the sum of its digits equal 36.. The sum of the digits plus product of the digits equals the number minus eight.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Find a two digit number such that the number itself minus the sum of its digits equal 36..
The sum of the digits plus product of the digits equals the number minus eight.
:
The two digits, a & b
10a + b = the number
:
Write an equation for each statement.
:
"the number itself minus the sum of its digits equal 36.."
10a + b - (a+b) = 36
10a + b - a - b = 36
9a = 36
a = 36/9
a = 4
:
"The sum of the digits plus product of the digits equals the number minus eight."
a + b + ab = 10a + b - 8
ab = 10a - a + b - b - 8
ab = 9a - 8
from the 1st statement we know a = 4
4b = 9(4) - 8
4b = 36 - 8
4b = 28
b = 28/4
b = 7
therefore:
47 is the number
:
:
You can confirm this yourself by using this number in the given statements

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