Question

1. a boarding kennel mixes dry dog food and wet dog food to feed the dogs. the table shows the mixture for different amounts.

dry dog food (cups)	wet dog food (oz)
6	3
9	4.5
?	5.5

(a) (5 points) is the relationship between the amount of dry dog food and the amount of wet dog food proportional? (use the first three rows of data to answer this question.) show your work and explain. you must show all your work to receive all credit.
(b) (5 points) how much dry dog food is used with 5.5 oz of wet dog food? show your work. you must show all your work to receive all credit.

Explanation:

Step1: Check proportionality (row1)

Calculate ratio of dry to wet:
$\frac{4.5}{2.25} = 2$

Step2: Check proportionality (row2)

Calculate ratio of dry to wet:
$\frac{6}{3} = 2$

Step3: Check proportionality (row3)

Calculate ratio of dry to wet:
$\frac{9}{4.5} = 2$

Step4: Explain proportionality

All ratios are equal (constant = 2), so the relationship is proportional.

Step5: Find dry food for 5.5 oz wet

Use the proportionality constant:
$\text{Dry food} = 2 \times 5.5$

Answer:

(a) The relationship is proportional. All pairs have a constant ratio of dry to wet food equal to 2, meaning dry food is always twice the amount of wet food.
(b) 11 cups