(a) To determine if the relationship between the amount of dry dog food and the amount of wet dog food is proportional, we need to check if the ratio of dry dog food to wet dog food is constant for all the given data.
We have the following pairs from the table:
- (4.5 cups, 1.5 oz)
- (6 cups, 2 oz)
- (9 cups, 3 oz)
Let's calculate the ratios:
- For the first pair: [tex]\( \frac{4.5}{1.5} = 3.0 \)[/tex]
- For the second pair: [tex]\( \frac{6}{2} = 3.0 \)[/tex]
- For the third pair: [tex]\( \frac{9}{3} = 3.0 \)[/tex]
Since all the calculated ratios are equal (3.0), we can conclude that the relationship between the amount of dry dog food and the amount of wet dog food is proportional.
(b) To find out how much dry dog food is used with 5.5 oz of wet dog food, we can use the constant ratio we found in part (a), which is 3.0.
Let [tex]\( x \)[/tex] be the amount of dry dog food used with 5.5 oz of wet dog food. We know from part (a) that the ratio [tex]\( \frac{\text{dry dog food}}{\text{wet dog food}} = 3.0 \)[/tex].
So,
[tex]\[ \frac{x}{5.5} = 3.0 \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = 3.0 \times 5.5 = 16.5 \][/tex]
Therefore, with 5.5 oz of wet dog food, 16.5 cups of dry dog food is used.
