Question

Which situation represents a proportional relationship?

Question 4 options:

A. The cost of purchasing a basket of apples for $1.25 per pound plus $5.00 for the basket


B. The cost of purchasing bananas for $5.00 per box of bananas with the delivery charge of $3.00


C. The cost of purchasing limes for $ 0.65 per pound with a coupon for $1.00 off the total cost


D. The cost of purchasing avocados for $1.75 per pound plus a shipping fee of $0.16 per pound.

Answer 1

D. The cost of purchasing avocados for $1.75 per pound plus a shipping fee of $0.16 per pound.

Explanation:

A linear relationship is of the form
`y=mx+b`, where,
`m` is the unit rate and
`b` is the fixed value (constant).

For a proportional relationship, the value of
`b=0` and thus it is of the form
`y=mx`

Let us check each option and express it in the form above.

Option A:

Given:

Unit rate of purchasing a basket of apples,
`m=\$ 1.25`

Fixed price for the basket,
`b=\$ 5`

Since,
`b \\e 0`, therefore, it is not a proportional relationship.

Option B:

Given:

Unit rate of purchasing a banana,
`m=\$ 5`

Fixed price for the box,
`b=\$ 3`

Since,
`b \\e 0`, therefore, it is not a proportional relationship.

Option C:

Given:

Unit rate of purchasing a lime,
`m=\$ 0.65`

Discount from total cost,
`b=\$ 1`

Since,
`b \\e 0`, therefore, it is not a proportional relationship.

Option D:

Given:

Unit rate of purchasing an avocado =
`\$ 1.75`

Unit rate of shipping =
`\$ 0.16`

Therefore, total cost per pound is the sum of the unit rates of purchasing and shipping. So,

Total cost of avocados per pound,
`m=1.75+0.16=\$ 1.91`

There is no fixed cost on this. So,
`b=0`

Since,
`b = 0`, therefore, it is a proportional relationship.

Therefore, the correct option is D.