Question

the sum of two numbers is 30. the difference of the two numbers is 4. what is the lesser number? 13 17 14 16

Explanation:

Step1: Define variables

Let the two numbers be \( x \) (greater) and \( y \) (lesser). So we have two equations: \( x + y = 30 \) and \( x - y = 4 \).

Step2: Solve the system of equations

Add the two equations together: \( (x + y) + (x - y) = 30 + 4 \). Simplifying the left side gives \( 2x \), and the right side is \( 34 \). So \( 2x = 34 \), which means \( x = 17 \).

Step3: Find the lesser number

Substitute \( x = 17 \) into \( x + y = 30 \). So \( 17 + y = 30 \). Subtract 17 from both sides: \( y = 30 - 17 = 13 \)? Wait, no, wait. Wait, if we check the difference: \( 17 - 13 = 4 \), and sum is \( 17 + 13 = 30 \). But wait, the options include 13, 17, 14, 16. Wait, maybe I made a mistake. Wait, let's check again. Wait, maybe the two numbers: let's let the lesser number be \( y \), greater be \( x \). So \( x + y = 30 \), \( x - y = 4 \). Adding the two equations: \( 2x = 34 \), so \( x = 17 \), then \( y = 30 - 17 = 13 \). But wait, 13 and 17: sum is 30, difference is 4. But wait, the options have 13, 17, 14, 16. Wait, maybe I messed up. Wait, let's check the options. Let's test each option. Let's take 13: then the other number is 30 - 13 = 17. Difference is 17 - 13 = 4. That works. Wait, but 13 is an option. Wait, but let's check 14: 30 - 14 = 16. Difference is 16 - 14 = 2. Not 4. 16: 30 - 16 = 14. Difference is 2. 17: 30 - 17 = 13. Difference is 4. So the lesser number is 13? Wait, but 13 is an option. Wait, but the problem says "the lesser number". So 13 is less than 17. So the answer should be 13? Wait, but let me check again. Wait, the equations: \( x + y = 30 \), \( x - y = 4 \). Solving: add the two equations: \( 2x = 34 \), so \( x = 17 \), then \( y = 30 - 17 = 13 \). So the lesser number is 13. But wait, the options have 13 as the first option. So that's correct.

Wait, but earlier I thought maybe I made a mistake, but no. So the lesser number is 13. Wait, but let's confirm. 13 + 17 = 30, 17 - 13 = 4. Perfect. So the lesser number is 13.

Answer:

13