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.

GPT-4o mini · Answer

To determine which table represents a proportional relationship, we need to check if the ratio of price to bundles is constant across all entries in the table. A proportional relationship has the same unit rate for all entries.

Let's calculate the price per bundle for each table.

Table A:

15 bundles: $45 ⇒ $45 / 15 = $3
25 bundles: $75 ⇒ $75 / 25 = $3
35 bundles: $105 ⇒ $105 / 35 = $3
50 bundles: $150 ⇒ $150 / 50 = $3
75 bundles: $225 ⇒ $225 / 75 = $3

All ratios are $3. This table represents a proportional relationship.

Table B:

15 bundles: $60 ⇒ $60 / 15 = $4
25 bundles: $100 ⇒ $100 / 25 = $4
35 bundles: $140 ⇒ $140 / 35 = $4
50 bundles: $200 ⇒ $200 / 50 = $4
75 bundles: $225 ⇒ $225 / 75 = $3

The first four ratios are $4, but the last one is $3. This table does not represent a proportional relationship.

Table C:

15 bundles: $45 ⇒ $45 / 15 = $3
25 bundles: $75 ⇒ $75 / 25 = $3
35 bundles: $105 ⇒ $105 / 35 = $3
50 bundles: $140 ⇒ $140 / 50 = $2.8
75 bundles: $205 ⇒ $205 / 75 = $2.7333...

The first three ratios are $3, but the other two are not. This table does not represent a proportional relationship.

Table D:

15 bundles: $50 ⇒ $50 / 15 = $3.3333...
25 bundles: $80 ⇒ $80 / 25 = $3.2
35 bundles: $110 ⇒ $110 / 35 = $3.142857...
50 bundles: $155 ⇒ $155 / 50 = $3.1
75 bundles: $230 ⇒ $230 / 75 = $3.0667...

None of these ratios are the same. This table does not represent a proportional relationship.

Conclusion:

The only table that represents a proportional relationship is Table A.