The average weight of 10 boys is 77.0 pounds. If the youngest boy is excluded, the average weight of the 9 remaining boys is 78.0 pounds. What is the weight, in pounds, of the youn... The average weight of 10 boys is 77.0 pounds. If the youngest boy is excluded, the average weight of the 9 remaining boys is 78.0 pounds. What is the weight, in pounds, of the youngest boy?
Understand the Problem
The question is asking for the weight of the youngest boy based on the average weight of ten boys and the average weight of the nine remaining boys after excluding the youngest. We will calculate the total weight of the ten boys and then isolate the youngest boy's weight.
Answer
68 pounds
Answer for screen readers
The weight of the youngest boy is (68) pounds.
Steps to Solve
- Calculate the Total Weight of All Boys
The average weight of 10 boys is 77.0 pounds. Hence, the total weight of all 10 boys can be calculated as:
$$ \text{Total Weight} = \text{Average Weight} \times \text{Number of Boys} = 77.0 \times 10 = 770 \text{ pounds} $$
- Calculate the Total Weight of the Remaining Boys
The average weight of the remaining 9 boys (after excluding the youngest) is 78.0 pounds. Therefore, their total weight is:
$$ \text{Total Weight of 9 Boys} = \text{Average Weight of 9 Boys} \times \text{Number of Boys} = 78.0 \times 9 = 702 \text{ pounds} $$
- Find the Weight of the Youngest Boy
The weight of the youngest boy can be found by subtracting the total weight of the 9 boys from the total weight of all boys:
$$ \text{Weight of Youngest Boy} = \text{Total Weight} - \text{Total Weight of 9 Boys} = 770 - 702 = 68 \text{ pounds} $$
The weight of the youngest boy is (68) pounds.
More Information
The problem illustrates how to use averages to derive individual weights when given total averages. This emphasizes the relationships between total weight and average weight, making it a practical example of basic algebraic manipulation.
Tips
- Confusing the total number of boys (10 vs. 9) when calculating average weights.
- Forgetting to convert the average back into a total weight when necessary.
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