Question

Jocelyn was shopping at a farmer's market. She observed the prices of cucumbers at several stands. Which set of prices shows a proportional relationship in the pricing of cucumbers?

A) 5 cucumbers for 2.50, 10 cucumbers for 4.00, 15 cucumbers for 5.50, 20 cucumbers for 7.00
B) 5 cucumbers for 2.50, 10 cucumbers for 4.50, 15 cucumbers for 6.50, 20 cucumbers for 8.50
C) 5 cucumbers for 2.00, 10 cucumbers for 4.00, 15 cucumbers for 6.00, 20 cucumbers for 8.00
D) 5 cucumbers for 1.50, 10 cucumbers for 3.00, 15 cucumbers for 6.00, 20 cucumbers for 12.00

Answer 1

Set C, with prices of 5 cucumbers for $2.00, 10 for $4.00, 15 for $6.00, and 20 for $8.00, shows a proportional relationship because the cost per cucumber is constant at $0.40 each.

Step-by-step explanation:

Jocelyn is analyzing prices of cucumbers at a farmer's market to determine which set of prices shows a proportional relationship. A proportional relationship occurs when two quantities have a constant ratio or unit rate. To find this, the cost per cucumber should be the same in every case.

• Set A: 5 cucumbers for $2.50, 10 for $4.00, 15 for $5.50, 20 for $7.00.
• Set B: 5 cucumbers for $2.50, 10 for $4.50, 15 for $6.50, 20 for $8.50.
• Set C: 5 cucumbers for $2.00, 10 for $4.00, 15 for $6.00, 20 for $8.00.
• Set D: 5 cucumbers for $1.50, 10 for $3.00, 15 for $6.00, 20 for $12.00.

Calculating the unit price for each option:

• Set A: $2.50/5 = $0.50 each, $4.00/10 = $0.40 each, $5.50/15 = $0.366 each, $7.00/20 = $0.35 each.
• Set B: $2.50/5 = $0.50 each, $4.50/10 = $0.45 each, $6.50/15 = $0.433 each, $8.50/20 = $0.425 each.
• Set C: $2.00/5 = $0.40 each, $4.00/10 = $0.40 each, $6.00/15 = $0.40 each, $8.00/20 = $0.40 each.
• Set D: $1.50/5 = $0.30 each, $3.00/10 = $0.30 each, $6.00/15 = $0.40 each, $12.00/20 = $0.60 each.

Only Set C maintains the same unit price, thus showing a proportional relationship.