SOLUTION: A two digit counting number has a value that is 7 more than 6 times the sum of its digits. If the units digit is 3 less than the tens digit, what is the number?

Question 1044100: A two digit counting number has a value that is 7 more than 6 times the sum of its digits. If the units digit is 3 less than the tens digit, what is the number?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let a = the 10's digit
let b = the units
then
10a+b = the number
:
Write an equation for each statement
:
A two digit counting number has a value that is 7 more than 6 times the sum of its digits.
10a + b = 6(a+b) + 7
10a + b = 6a + 6b + 7
10a - 6a = 6b - b + 7
4a = 5b + 7
:
If the units digit is 3 less than the tens digit,
b = a - 3
:
Replace b in the 1st equation
4a = 5(a-3) + 7
4a = 5a - 15 + 7
4a - 5a = -8
-a = -8
a = 8
find b
b = 8 - 3
b = 5
:
what is the number? 85 is the number
:
:
Check this in the first statement simplified equation
4(8) = 5(5) - 7
32 = 25 - 7
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