Question 1 of 25intermediate🔧 ApplyNumerical3 marks

The sum of four consecutive numbers is 34. What are these numbers?

Correct Answer

Given: Sum of four consecutive numbers = 34.

Step 1: Let the four consecutive numbers be nn, n+1n+1, n+2n+2, and n+3n+3.

Step 2: Write the sum equation:

n+(n+1)+(n+2)+(n+3)=34n + (n+1) + (n+2) + (n+3) = 34

Step 3: Simplify:

4n+6=344n + 6 = 34

Step 4: Solve:

4n=284n = 28 n=7n = 7

Step 5: The numbers are 7, 8, 9, and 10.

Verification: 7+8+9+10=347 + 8 + 9 + 10 = 34

Answer: The four consecutive numbers are 7, 8, 9, and 10.

Exercise: Figure it Out (Section 1) | Q: 1 | (Page Page 11)
For More Understanding

Explanation

Let the four consecutive numbers be n, n+1, n+2, and n+3. Their sum equals n + (n+1) + (n+2) + (n+3) = 4n + 6. Setting this equal to 34: 4n + 6 = 34, so 4n = 28, giving n = 7. Therefore, the numbers are 7, 8, 9, and 10. Verification: 7 + 8 + 9 + 10 = 34.

Solution Steps

  1. Step 1: Let the four consecutive numbers be n, n+1, n+2, n+3.

  2. Step 2: Write the sum equation: n + (n+1) + (n+2) + (n+3) = 34

  3. Step 3: Simplify: 4n + 6 = 34

  4. Step 4: Solve: 4n = 28, so n = 7

  5. Step 5: The numbers are 7, 8, 9, 10

Next