SOLUTION: A two digit counting number has a value of 8 times the sum of its digits. If 6 times the units digit is 5 more than the tens digits, what is the number?

Question 147405: A two digit counting number has a value of 8 times the sum of its digits. If 6 times the units digit is 5 more than the tens digits, what is the number?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A two digit counting number has a value of 8 times the sum of its digits. If 6 times the units digit is 5 more than the tens digits, what is the number?
.
Let x = "units" digit
and y = "tens" digit
.
Since we have two unknowns, we'll need two equations.
.
From:
"A two digit counting number has a value of 8 times the sum of its digits."
we get equation 1:
10y + x = 8(x+y)
.
From:
"6 times the units digit is 5 more than the tens digits"
we get equation 2:
6x - 5 = y
.
From equation 2, we see that y is equal to (6x+5) -- substitute this into equation 1 and solve for x:
10y + x = 8(x+y)
10(6x-5) + x = 8(x+(6x-5))
(60x-50) + x = 8(7x-5)
61x-50 = 56x-40
5x = 10
x = 2
.
To find y, substitute the above into equation 2:
6x - 5 = y
6(2) - 5 = y
12 - 5 = y
7 = y
.
Your 2 digit number is: 72

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