Tianna Y. answered • 04/19/19
Experienced Tutor Specialized with K-6
This problem can be solved using various methods but one of the better methods to implement is a version trial and error (this method is also known as guess and check).
First, let's break down the key words/phrases in the problem it's self to help us find a starting point. To do this let's look at the first portion of the sentence which states, "The sum of the digits of a certain two digit number is 7." The key words/phrases includes sum, two digit number, and 7. Now let's look at the rest of the sentence which states, "reversing it's digits increases the number by 9." Here the key words/phrases includes reversing, increases, and 9.
Now we can take the first portion of the sentence's key words/phrases to give us a starting point. Sum means addition which means if we add each digit in a two digit number, it needs to equal 7. We can start by listing off all of the numbers that added together equals 7.
1 + 6 = 7
2 + 5 = 7
3 + 4 = 7
4 + 3 = 7
5 + 2 = 7
6 + 1 = 7
Now we have a list of all possible two digit numbers that meet the requirements for the first part of the requirements. This list includes: 16, 25, 34, 43, 52, and 61.
From here we can pair the two digit numbers together based upon if they contain the same individual digits. This means 16 gets paired with 61; 25 paired with 52; 34 paired with 43.
The key words/phrases in the second portion of the requirements to sift through these pairings to find the right pair. The requirement means the reversing of digits will increase (in other words, grow bigger) by 9. To see which pair is the right one, we can subtract the larger number by the smaller number of each grouping.
61 - 16 = 45
52 - 25 = 27
43 - 34 = 9
From this whole process we find that the answer is 34. When you add each of these digits together they equal 7 (3 + 4 = 7) but when you reverse the order (34 becomes 43) the entire value of the number increases by 9.
I hope this was helpful! Good luck!
