Math Problem Statement

The average of three numbers is 30. Two of the numbers is 28 and 35. What is the third number?

Solution

To find the third number when given the average and two of the three numbers, we can use the following steps:

  1. Understand the average: The average of three numbers is given by the formula: Average=Sum of the numbersNumber of numbers\text{Average} = \frac{\text{Sum of the numbers}}{\text{Number of numbers}} In this case, the average is 30, and the number of numbers is 3.

  2. Find the sum of the numbers: Using the average formula, we can find the sum of the three numbers: Sum of the numbers=Average×Number of numbers=30×3=90\text{Sum of the numbers} = \text{Average} \times \text{Number of numbers} = 30 \times 3 = 90

  3. Sum of known numbers: The two known numbers are 28 and 35. Calculate their sum: 28+35=6328 + 35 = 63

  4. Find the third number: Subtract the sum of the known numbers from the total sum to find the third number: Third number=Sum of the numbersSum of known numbers=9063=27\text{Third number} = \text{Sum of the numbers} - \text{Sum of known numbers} = 90 - 63 = 27

Thus, the third number is 2727.

Would you like more details or have any questions?

Here are some related questions for further practice:

  1. If the average of four numbers is 25 and three of the numbers are 20, 30, and 25, what is the fourth number?
  2. The average of five numbers is 50. If four of the numbers are 45, 55, 50, and 60, what is the fifth number?
  3. The average of three numbers is 40. If one of the numbers is 50 and another is 45, what is the third number?
  4. If the sum of four numbers is 120 and three of the numbers are 25, 30, and 20, what is the fourth number?
  5. The average of three numbers is 35. If two of the numbers are 40 and 30, what is the third number?

Tip: When dealing with averages, remember that the sum of the numbers can be easily found by multiplying the average by the number of terms.

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Math Problem Analysis

Mathematical Concepts

Averages
Basic Arithmetic

Formulas

Average = (Sum of numbers) / (Number of numbers)

Theorems

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Suitable Grade Level

Grades 5-6