Mr. Kelsey just opened a T‑shirt shop and is determining what to charge for bundles of shirts. Which table of prices represents a proportional relationship?

Question

A.
The table shows 'shirt bundles' in the first column and 'price of bundle' in the second column. 15 bundles is priced 45 dollars, 25 bundles is priced 75 dollars, 35 bundles is priced 105 dollars, 50 bundles is priced 150 dollars, and 75 bundles is priced 225 dollars.

B.
The table shows 'shirt bundles' in the first column and 'price of bundle' in the second column. 15 bundles is priced 60 dollars, 25 bundles is priced 100 dollars, 35 bundles is priced 140 dollars, 50 bundles is priced 200 dollars, and 75 bundles is priced 225 dollars.

C.
The table shows 'shirt bundles' in the first column and 'price of bundle' in the second column. 15 bundles is priced 45 dollars, 25 bundles is priced 75 dollars, 35 bundles is priced 105 dollars, 50 bundles is priced 140 dollars, and 75 bundles is priced 205 dollars.

D.
The table shows 'shirt bundles' in the first column and 'price of bundle' in the second column. 15 bundles is priced 50 dollars, 25 bundles is priced 80 dollars, 35 bundles is priced 110 dollars, 50 bundles is priced 155 dollars, and 75 bundles is priced 230 dollars.

Answer 1

To determine which table represents a proportional relationship, we need to check whether the ratio of the price to the number of bundles remains constant.

We can calculate the price per bundle for each option.

Option A:

• 15 bundles for $45: \( \frac{45}{15} = 3 \)
• 25 bundles for $75: \( \frac{75}{25} = 3 \)
• 35 bundles for $105: \( \frac{105}{35} = 3 \)
• 50 bundles for $150: \( \frac{150}{50} = 3 \)
• 75 bundles for $225: \( \frac{225}{75} = 3 \)

The ratio is consistent (3) for all bundles. Thus, A represents a proportional relationship.

Option B:

• 15 bundles for $60: \( \frac{60}{15} = 4 \)
• 25 bundles for $100: \( \frac{100}{25} = 4 \)
• 35 bundles for $140: \( \frac{140}{35} = 4 \)
• 50 bundles for $200: \( \frac{200}{50} = 4 \)
• 75 bundles for $225: \( \frac{225}{75} = 3 \)

The ratio changes (from 4 to 3). So, B does not represent a proportional relationship.

Option C:

• 15 bundles for $45: \( \frac{45}{15} = 3 \)
• 25 bundles for $75: \( \frac{75}{25} = 3 \)
• 35 bundles for $105: \( \frac{105}{35} = 3 \)
• 50 bundles for $140: \( \frac{140}{50} = 2.8 \)
• 75 bundles for $205: \( \frac{205}{75} \approx 2.733 \)

The ratios are inconsistent. So, C does not represent a proportional relationship.

Option D:

• 15 bundles for $50: \( \frac{50}{15} \approx 3.33 \)
• 25 bundles for $80: \( \frac{80}{25} = 3.2 \)
• 35 bundles for $110: \( \frac{110}{35} \approx 3.14 \)
• 50 bundles for $155: \( \frac{155}{50} = 3.1 \)
• 75 bundles for $230: \( \frac{230}{75} \approx 3.07 \)

The ratios are inconsistent. So, D does not represent a proportional relationship.

In conclusion, the only option that represents a proportional relationship is Option A.