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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 ?

Explanation	Calculations	Help
$We start by defining a variable for the total number of pieces of clothing across all 8 boxes and translate the given average.$	$T = 8 c$	Theory & Tactics Method Card TRANS1-A Click to view full details Theory & Tactics Method Card TRANS3-F Click to view full details
$We compute the new total after removing the 12-piece box and adding the 22-piece box.$	$T_{new} = T - 12 + 22$	Theory & Tactics Method Card TRANS1-C Click to view full details Theory & Tactics Method Card TRANS1-D Click to view full details
$We find the new average by dividing the updated total by 8 and then simplify the fraction.$	$\frac{T _{new}}{8} = \frac{8 c + 10}{8} = c + \frac{10}{8} = c + \frac{2 \times 5}{2 \times 4} = c + \frac{5}{4}$	Theory & Tactics Method Card FDPR2-A Click to view full details

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The new average is c + \frac{5}{4}, so the correct answer is choice B.

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 ?

Explanation	Calculations	Help
$We start by defining a variable for the total number of pieces of clothing across all 8 boxes and translate the given average.$	$T = 8 c$	Theory & Tactics Method Card TRANS1-A Click to view full details Theory & Tactics Method Card TRANS3-F Click to view full details
$We compute the new total after removing the 12-piece box and adding the 22-piece box.$	$T_{new} = T - 12 + 22$	Theory & Tactics Method Card TRANS1-C Click to view full details Theory & Tactics Method Card TRANS1-D Click to view full details
$We find the new average by dividing the updated total by 8 and then simplify the fraction.$	$\frac{T _{new}}{8} = \frac{8 c + 10}{8} = c + \frac{10}{8} = c + \frac{2 \times 5}{2 \times 4} = c + \frac{5}{4}$	Theory & Tactics Method Card FDPR2-A Click to view full details

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The new average is c + \frac{5}{4}, so the correct answer is choice B.