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Calculate the number of apples in the 12th bag. Show your working.

There are 12 bags of apples on a market stall. The mean number of apples in each bag is 8.

The table shows the number of apples in 11 of the bags:

[tex]\[
\begin{tabular}{|c|c|}
\hline
Number of apples & Frequency \\
\hline
6 & 1 \\
\hline
7 & 4 \\
\hline
8 & 2 \\
\hline
9 & 3 \\
\hline
10 & 1 \\
\hline
\end{tabular}
\][/tex]

First, find the total number of apples in the 11 bags:

[tex]\[
(6 \times 1) + (7 \times 4) + (8 \times 2) + (9 \times 3) + (10 \times 1) = 6 + 28 + 16 + 27 + 10 = 87
\][/tex]

Next, calculate the total number of apples for 12 bags with a mean of 8 apples per bag:

[tex]\[
8 \times 12 = 96
\][/tex]

Finally, find the number of apples in the 12th bag:

[tex]\[
96 - 87 = 9
\][/tex]

Sagot :

GinnyAnswer
To find the number of apples in the 12th bag, follow these steps:

1. Calculate the total number of apples in the first 11 bags:
- We use the table to identify the number of apples in each bag and their corresponding frequencies:
[tex]\[ \begin{aligned} &\text{Number of apples in 6-apple bags} &= 6 \times 1 &= 6 \\ &\text{Number of apples in 7-apple bags} &= 7 \times 4 &= 28 \\ &\text{Number of apples in 8-apple bags} &= 8 \times 2 &= 16 \\ &\text{Number of apples in 9-apple bags} &= 9 \times 3 &= 27 \\ &\text{Number of apples in 10-apple bags} &= 10 \times 1 &= 10 \\ \end{aligned} \][/tex]

- Sum these amounts to find the total number of apples in the first 11 bags:
[tex]\[ 6 + 28 + 16 + 27 + 10 = 87 \][/tex]

2. Calculate the total number of apples in all 12 bags using the mean:
- The mean number of apples per bag is given as 8. Therefore, the total number of apples in all 12 bags is:
[tex]\[ 8 \times 12 = 96 \][/tex]

3. Determine the number of apples in the 12th bag:
- To find the number of apples in the 12th bag, subtract the total number of apples in the first 11 bags from the overall total number of apples:
[tex]\[ 96 - 87 = 9 \][/tex]

Thus, the number of apples in the 12th bag is [tex]\( 9 \)[/tex].
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