Question
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.
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.
Answers
GPT-4o mini
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.**
**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.**