SOLUTION: The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number?
I know that the answer is 34, and I know that one
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Question 130266: The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number?
I know that the answer is 34, and I know that one of the equations is x+y=7, but I do not know the other part to the system of equations. Thanks for helping me!!!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
There are actually two ways to solve this problem. Either way, your first equation is correct. .
The first way is to derive two additional equations.
If x is the 10s digit and y is the ones digit then 10x plus y equals the number.
Now, if we reverse the digits, y becomes the 10s digit and x becomes the ones digit and the number is increased by 9, so:
Add -9 to both sides of this last equation to get . Now we have two things that equal n so we can set these two expressions equal to each other:
Add this last equation to your very first equation () term by term:
From we get , therefore the number is 34.
The second way to solve the problem is to realize that the difference between any two-digit number and the result of reversing the digits of that two-digit number is a multiple of nine, and that the multiplier of 9 is the difference between the two digits (for example 25 and 52 differ by 27, 2 and 5 differ by 3 and 27 is 3 times 9). Since reversing the digits in this problem resulted in a number that was 9 larger, the 10s digit had to be 1 smaller than the ones digit. This way you could have written directly and solved from there.
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