SOLUTION: The sum of the digits of a two-digit number is 7. If the digits are reversed,the new number increased by 3 less than 4 times the original number. Find the original number.

Question 1089478: The sum of the digits of a two-digit number is 7. If the digits are reversed,the new number increased by 3 less than 4 times the original number. Find the original 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
:
The sum of the digits of a two-digit number is 7.
a + b = 7
b = (7-a), use this form for substitution
If the digits are reversed, the new number increased by 3 less than 4 times the original number.
10b + a = 4(10a + b) - 3
10b + a = 40a + 4b - 3
10b - 4b = 40a - a - 3
6b = 39a - 3
replace b with (7-a)
6(7-a) = 39a - 3
42 - 6a = 39a - 3
42 + 3 = 39a + 6a
45 = 45a
a = 1
then
b = 7 - 1
b = 6
:
Find the original: 16
:
:
you should check this for yourself in the 2nd statement
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