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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?
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Let x = "units" digit
and y = "tens" digit
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Since we have two unknowns, we'll need two equations.
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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)
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From:
"6 times the units digit is 5 more than the tens digits"
we get equation 2:
6x - 5 = y
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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
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To find y, substitute the above into equation 2:
6x - 5 = y
6(2) - 5 = y
12 - 5 = y
7 = y
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Your 2 digit number is: 72
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