Beth has a collection of 8 boxes of clothing for a charity, and the average (arithmetic mean)...

Question

Beth has a collection of 8 boxes of clothing for a charity, and the average (arithmetic mean) number of pieces of clothing per box is c. If she replaces a box in the collection that contains 12 pieces of clothing with a box that contains 22 pieces of clothing, what is the average number of pieces of clothing per box for the new collection, in terms of c ?

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B We start by defining a variable for the total number of pieces of clothing across all 8 boxes and translate the given average. T = 8c We compute the new total after removing the 12-piece box and adding the 22-piece box. T_new = T - 12 + 22 We find the new average by dividing the updated total by 8 and then simplify the fraction. T_new8 = 8c + 10/8 = c + 10/8 = c + 2524 = c + 5/4

Explanation	Calculations	Help
$We start by defining a variable for the total number of pieces of clothing across all 8 boxes and translate the given average.$	$T = 8 c$
$We compute the new total after removing the 12-piece box and adding the 22-piece box.$	$T_{new} = T - 12 + 22$
$We find the new average by dividing the updated total by 8 and then simplify the fraction.$	$\frac{T _{new}}{8} = \frac{8 c + 10}{8} = c + \frac{10}{8} = c + \frac{2 \times 5}{2 \times 4} = c + \frac{5}{4}$

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