Question

Two stores sell CDs in packages, as shown in the table below. Number of CDs in Package Cost Number of CDs in Package Cost CD Prices at Store A 1 $0.70 CD Prices at Store B 1 $0.60 12 $8.40 20 ? 20 ? 30 $18.00 45 $31.50 65 $39.00 If the rate at each store is constant, which statement correctly compares the cost of a package containing 20 CDs? The cost at Store A is $2.00 greater than at Store B. The cost at Store B is $2.00 greater than at Store A. The cost at Store A is $1.00 greater than at Store B.​

Answer 1

Based on their equations that models each proportional relationship for each store, the correct statement is: A.  The cost at Store A is $2.00 greater than at Store B.

How to Find the Constant Proportionality of a Proportional Relationship?

The constant of proportionality, k, is given as, y/x. The equation that models a relationship that has a constant (k), is expressed as y = kx.

The relationship between number of CDs in packages and its cost for each store is proportional because we are told the  rate at each store is constant.

Using a pair of values in each table, we can find the constant of proportionality (k) and the equation that models each table given.

Store A:

Constant of proportionality, k = y/x = 0.70/1 = 0.70

The equation for store A would be, y = 0.70x.

Store B:

Constant of proportionality, k = y/x = 0.60/1 = 0.60.

The equation for store A would be, y = 0.60x.

Find the cost of a package containing 20 CDs for store A and store D using their equations by substituting x = 20 into each of the equations:

Store A: y = 0.70(20) = $14

Store B: y = 0.60(20) = $12

The difference between both stores is: 14 - 12 = $2.

Therefore, based on their equations that models each proportional relationship for each store, the correct statement is: A.  The cost at Store A is $2.00 greater than at Store B.

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