Question

1. this table shows the amount of sugar in different volumes of orange juice.

	glass	bottle	carton	jug
sugar (grams)	24		96	384

a. complete the table to determine the amount of sugar in different - sized containers of orange juice.
b. explain why the relationship between the volume of orange juice and the amount of sugar is proportional

Explanation:

Part (a): Completing the Table

Step 1: Find the ratio of sugar to volume

First, we find the ratio of sugar (in grams) to volume (in oz) using the given values for Glass. For Glass, volume is 8 oz and sugar is 24 grams. So the ratio is $\frac{24}{8} = 3$ grams per oz. This means for each ounce of orange juice, there are 3 grams of sugar.

Step 2: Calculate sugar for Bottle

For Bottle, volume is 12 oz. Using the ratio (3 grams per oz), the sugar is $12 \times 3 = 36$ grams.

Step 3: Verify with Carton (optional, for check)

For Carton, volume is 32 oz. Sugar should be $32 \times 3 = 96$ grams, which matches the given value, so our ratio is correct.

Step 4: Calculate sugar for Jug

For Jug, volume is 128 oz. Sugar is $128 \times 3 = 384$ grams (which also matches the given "38N" - likely a typo for 384).

The relationship between volume of orange juice (in oz) and amount of sugar (in grams) is proportional because the ratio of sugar to volume is constant. For Glass: $\frac{24}{8} = 3$, Bottle: $\frac{36}{12} = 3$, Carton: $\frac{96}{32} = 3$, Jug: $\frac{384}{128} = 3$. Since the ratio (constant of proportionality) is the same for all containers, the two quantities are directly proportional (i.e., $y = kx$ where $y$ is sugar, $x$ is volume, and $k = 3$).

Answer:

(Completed Table):

Container	Volume (oz)	Sugar (grams)
Bottle	12	36
Carton	32	96
Jug	128	384

Part (b): Explaining Proportional Relationship