SOLUTION: 1.The sum of the digits of a two-digit number is 8. The number with the digits interchanged is 16 less than thrice the original number. Find the number. 2.the units digit of a two

Algebra ->  Proportions -> SOLUTION: 1.The sum of the digits of a two-digit number is 8. The number with the digits interchanged is 16 less than thrice the original number. Find the number. 2.the units digit of a two      Log On


   

Question 988820: 1.The sum of the digits of a two-digit number is 8. The number with the digits interchanged is 16 less than thrice the original number. Find the number.
2.the units digit of a two-digit number is one less than one-half the tens digit. The number with the digits interchanged is 5 more than thrice the sum of the digits. Help me thanks
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
For this kind of problem, I would start with
x= the tens digit
y= the ones digit
10x%2By= the value of the original number
10y%2Bx= the value of the number with the digits interchanged

1. The sum of the digits of a two-digit number is 8 translates as
x%2By=8 .
The number with the digits interchanged is 16 less than thrice the original number translates as
10y%2Bx=3%2A%2810x%2By%29-16 .
Now you have two equations. You can simplify the second one a bit:
10y%2Bx=3%2A%2810x%2By%29-16--->10y%2Bx=30x%2B3y-16--->10y%2Bx-30x-3y=-16--->7y-29x=-16--->29x-7y=16 .
system%28x%2By=8%2C29x-7y=16%29--->system%28y=8-x%2C29x-7y=16%29--->system%28y=8-x%2C29x-7%288-x%29=16%29
--->system%28y=8-x%2C29x-56%2B7x=16%29--->system%28y=8-x%2C36x-56=16%29--->system%28y=8-x%2C36x=16%2B56%29
--->system%28y=8-x%2C36x=72%29--->system%28y=8-x%2Cx=72%2F36%29--->system%28y=8-x%2Cx=2%29--->system%28y=8-2%2Cx=2%29--->highlight%28system%28y=6%2Cx=2%29%29

2. The units digit of a two-digit number is one less than one-half the tens digit translates as
y=%281%2F2%29x-1--->2y=2%28%281%2F2%29x-1%29--->2y=x-2--->2y%2B2=x .
The number with the digits interchanged is 5 more than thrice the sum of the digits translates as
10y%2Bx=3%28x%2By%29%2B5--->10y%2Bx=3x%2B3y%2B5--->10y%2Bx-3x-3y=5--->7y-2x=5 .
system%28x=2y%2B2%2C7y-2x=5%29--->system%28x=2y%2B2%2C7y-2%282y%2B2%29=5%29--->system%28x=2y%2B2%2C7y-4y-4=5%29
--->system%28x=2y%2B2%2C3y-4=5%29--->system%28x=2y%2B2%2C3y=5%2B4%29--->system%28x=2y%2B2%2C3y=9%29--->system%28x=2y%2B2%2Cy=9%2F3%29
--->system%28x=2y%2B2%2Cy=3%29--->system%28x=2%2A3%2B2%2Cy=3%29--->highlight%28system%28x=8%2Cy=3%29%29