Question
set 1. The average of the first three numbers was 42 . The average of the next seven numbery 59 was only 12 . What was the average of all ten numbers?
Ask by Byrd Elliott. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The average of all ten numbers is 21.
Solution
To find the average of all ten numbers, let's break down the information given:
1. **First Three Numbers:**
- **Average:** 42
- **Total Sum:** \( 3 \times 42 = 126 \)
2. **Next Seven Numbers:**
- **Average:** 12
- **Total Sum:** \( 7 \times 12 = 84 \)
3. **All Ten Numbers:**
- **Combined Sum:** \( 126 + 84 = 210 \)
- **Average:** \( \frac{210}{10} = 21 \)
**Answer:** The average of all ten numbers is **21**.
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Simplify this solution Extra Insights
To find the average of all ten numbers, we need to calculate the total sums of the groups of numbers. For the first three numbers with an average of 42, the total sum is: \( 3 \times 42 = 126 \). For the next seven numbers with an average of 12, the total sum is: \( 7 \times 12 = 84 \). Now, we'll add both sums together: \( 126 + 84 = 210 \). Now, we can find the average of all ten numbers: \( \text{Average} = \frac{\text{Total Sum}}{\text{Number of Items}} = \frac{210}{10} = 21 \). So, the average of all ten numbers is 21.
