Let's define the two-digit number as $10a + b$, where:

• $a$ is the tens digit
• $b$ is the ones digit

Step 1: Set Up Equations

1. The sum of the digits is 7: $a + b = 7$

2. Reversing the digits increases the number by 9: $10b + a = (10a + b) + 9$

Step 2: Solve for $a$ and $b$

Rewriting the second equation: $10b + a - 10a - b = 9$

$9b - 9a = 9$

$b - a = 1$

Step 3: Solve the System

We have the system:

1. $a + b = 7$
2. $b - a = 1$

Adding both equations:

$(a + b) + (b - a) = 7 + 1$

$2b = 8$

$b = 4$

Substituting $b = 4$ into $a + b = 7$:

$a + 4 = 7$

$a = 3$

Step 4: Find the Number

The number is:

$10(3) + 4 = 34$

Step 5: Verify

• The sum of the digits: $3 + 4 = 7$ ✅
• Reversing gives 43, which is 9 more than 34 ✅

Thus, the number is 34.

Would you like further explanations or another method?

Here are 5 related questions to practice:

1. A two-digit number has a sum of digits equal to 10. Reversing its digits decreases the number by 36. What is the number?
2. The sum of the digits of a two-digit number is 9, and reversing the digits results in a number 27 greater than the original. Find the number.
3. A two-digit number is 4 times the sum of its digits. What is the number?
4. The sum of the digits of a two-digit number is 11, and the difference between the number and its reversed form is 9. Find the number.
5. The difference between a two-digit number and the number obtained by reversing its digits is 45. The sum of its digits is 11. Find the number.

Tip:

When dealing with two-digit problems, define variables clearly and use equations systematically for an easier solution! 🚀