Question

1. attend to precision erin has 10 bags of apples. the following are the weights of the bags in pounds: 2\frac{3}{4}, 2\frac{1}{2}, 2\frac{1}{4}, 1\frac{1}{2}, 2\frac{1}{2}, 2\frac{1}{4}, 2\frac{1}{2}, 1\frac{1}{4}, 2\frac{1}{2}, 2\frac{1}{4}. write an expression that shows the average weight of a bag. evaluate the expression. ( - 1 ) + 2 ( \frac { 1 } { 2 } ) - 2 ( \frac { 3 } { 4 } ) using the

Explanation:

Step1: Find the sum of the weights

The formula for the average of a set of numbers is \(\frac{\text{Sum of numbers}}{\text{Number of numbers}}\). First, find the sum of the weights. There are 10 bags. The weights are \(2\frac{1}{2},2\frac{1}{2},2\frac{1}{4},1\frac{1}{4},2\frac{1}{2},2\frac{1}{2},1\frac{1}{4},2\frac{1}{2},2\frac{1}{4},2\frac{1}{4}\).
Convert the mixed - numbers to improper fractions:
\(2\frac{1}{2}=\frac{2\times2 + 1}{2}=\frac{5}{2}\), \(2\frac{1}{4}=\frac{2\times4+1}{4}=\frac{9}{4}\), \(1\frac{1}{4}=\frac{1\times4 + 1}{4}=\frac{5}{4}\).
The sum \(S=\frac{5}{2}+\frac{5}{2}+\frac{9}{4}+\frac{5}{4}+\frac{5}{2}+\frac{5}{2}+\frac{5}{4}+\frac{5}{2}+\frac{9}{4}+\frac{9}{4}\).
Group the terms:
\(S = 5\times\frac{5}{2}+3\times\frac{9}{4}+2\times\frac{5}{4}\).
\(S=\frac{25}{2}+\frac{27}{4}+\frac{10}{4}\).
Find a common denominator (4):
\(S=\frac{25\times2}{2\times2}+\frac{27 + 10}{4}=\frac{50}{4}+\frac{37}{4}=\frac{50 + 37}{4}=\frac{87}{4}\).

Step2: Calculate the average

Since the number of bags \(n = 10\), the average weight \(A=\frac{S}{n}\).
\(A=\frac{\frac{87}{4}}{10}\).
Using the rule \(\frac{a}{b}\div c=\frac{a}{b\times c}\), we have \(A=\frac{87}{4\times10}=\frac{87}{40}=2\frac{7}{40}\).
Another way:
The formula for the average of a set of numbers \(x_1,x_2,\cdots,x_n\) is \(\frac{1}{n}\sum_{i = 1}^{n}x_i\).
\(A=\frac{1}{10}(5\times2\frac{1}{2}+3\times2\frac{1}{4}+2\times1\frac{1}{4})\).
\(=\frac{1}{10}(5\times\frac{5}{2}+3\times\frac{9}{4}+2\times\frac{5}{4})\).
\(=\frac{1}{10}(\frac{25}{2}+\frac{27}{4}+\frac{10}{4})\).
\(=\frac{1}{10}(\frac{50 + 27+10}{4})\).
\(=\frac{1}{10}\times\frac{87}{4}=\frac{87}{40}=2\frac{7}{40}\).

Answer:

The expression is \(\frac{1}{10}(5\times2\frac{1}{2}+3\times2\frac{1}{4}+2\times1\frac{1}{4})\) and the average weight is \(2\frac{7}{40}\) pounds.