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Two stores sell CDs in packages, as shown in the table below.

CD Prices at Store A
Number of CDs in Package
1
12
20
45
Cost
$0.70
$8.40
?
$31.50

CD Prices at Store B
Number of CDs in Package
1
20
30
65
Cost
$0.60
?
$18.00
$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.
The cost at Store B is $1.00 greater than at Store A.

1 answer

To compare the cost of a package containing 20 CDs at Store A and Store B, we first need to determine the cost per CD for each store.

Calculating the cost per CD at Store A:

  1. For 1 CD, the cost is $0.70. \[ \text{Cost per CD} = \frac{0.70}{1} = 0.70 \]

  2. For 12 CDs, the cost is $8.40. \[ \text{Cost per CD} = \frac{8.40}{12} = 0.70 \]

  3. The cost for 20 CDs is unknown. We assume cost per CD remains constant at $0.70. \[ \text{Cost for 20 CDs} = 20 \times 0.70 = 14.00 \]

  4. For 45 CDs, the cost is $31.50. \[ \text{Cost per CD} = \frac{31.50}{45} = 0.70 \]

So, the cost of a package containing 20 CDs at Store A is $14.00.

Calculating the cost per CD at Store B:

  1. For 1 CD, the cost is $0.60. \[ \text{Cost per CD} = \frac{0.60}{1} = 0.60 \]

  2. The cost for 20 CDs is unknown; we will calculate it based on the 30 CDs cost provided.

  3. For 30 CDs, the cost is $18.00. \[ \text{Cost per CD} = \frac{18.00}{30} = 0.60 \]

  4. For 65 CDs, the cost is $39.00. \[ \text{Cost per CD} = \frac{39.00}{65} = 0.60 \]

So, we assume the cost per CD remains constant at $0.60 for Store B.

Now, to find the cost of 20 CDs at Store B: \[ \text{Cost for 20 CDs} = 20 \times 0.60 = 12.00 \]

Comparison of costs:

  • Store A (20 CDs): $14.00
  • Store B (20 CDs): $12.00

Thus, the difference is: \[ 14.00 - 12.00 = 2.00 \]

Therefore, the correct statement is: The cost at Store A is $2.00 greater than at Store B.