SOLUTION: Hi Tutor, please me help on the below 2 word problems 1. The sum of the digits of a two-digit number is 10. If the digits are reversed, the number is increased by 36. What is th

Question 137102: Hi Tutor, please me help on the below 2 word problems
1. The sum of the digits of a two-digit number is 10. If the digits are reversed, the number is increased by 36. What is the original number?
2. The sum of the digits of a two-digit number ois 12. If the digits are reversed, the new number is 18 more than the original number. Find the original number.
Thank you..
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1. The sum of the digits of a two-digit number is 10. If the digits are reversed, the number is increased by 36. What is the original number?
:
Let the two digits be x & y
x + y = 10
y = (10-x); arranged to be used for substitution
:
Write an equation for the statement
"If the digits are reversed, the number is increased by 36."
10x + y = 10y + x - 36
:
combine x's on the left and y's on the right
10x - x = 10y - y - 36
:
Simplify divide by 4:
9x = 9y - 36
x = y - 4
:
Substitute (10-x) for y (from the 1st equation):
x = 10 - x - 4
x + x = 10 - 4
2x = 6
x = 3
Therefore the two digit number is 37 (Reversed; 73 which is 36 more than 37)
:
:
Do exactly the same with this one
2. The sum of the digits of a two-digit number is 12.
x + y = 12
y = (12 - x)
:
If the digits are reversed, the new number is 18 more than the original number.
10x + y = 10y + x - 18
:
Find the original number.
:
See if you can do this now. Email me if you have difficulty
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