Question

1. a typical soda contains between 25 to 35 grams of sugar per 12 ounce can depending on the brand and flavor. a few examples are listed below. by comparison, a typical sugar packet that you might find at a restaurant contains 1.9 grams of sugar.

soda	sugar per 12 ounce can
mt. dew	46.5 grams
sunkist	52 grams

a) how many packets of sugar are in one 12 ounce can of sunkist?
b) lets say you drink 2 mt. dews a day, one 20 ounce bottle for breakfast and one 16 ounce bottle in the afternoon. how many packets of sugar are you getting just from the soda?

Explanation:

Step1: Calculate sugar - packets in Sunkist

We know that a Sunkist 12 - ounce can has 52 grams of sugar and a sugar packet has 1.9 grams of sugar. We use division to find the number of packets.
$n_1=\frac{52}{1.9}\approx 27.37$

Step2: Calculate sugar - grams in Mt. Dew bottles

First, find the ratio of sugar in a non - 12 - ounce bottle compared to a 12 - ounce bottle. For a 20 - ounce Mt. Dew bottle, let the amount of sugar be $x_1$. Since the amount of sugar is proportional to the volume, $\frac{x_1}{20}=\frac{46.5}{12}$, so $x_1=\frac{46.5\times20}{12}=77.5$ grams. For a 16 - ounce Mt. Dew bottle, let the amount of sugar be $x_2$. Then $\frac{x_2}{16}=\frac{46.5}{12}$, so $x_2=\frac{46.5\times16}{12}=62$ grams.

Step3: Calculate total sugar in Mt. Dew bottles

The total amount of sugar from the two Mt. Dew bottles is $x = x_1 + x_2=77.5+62 = 139.5$ grams.

Step4: Calculate sugar - packets in Mt. Dew bottles

We divide the total sugar by the amount of sugar in one packet. The number of packets $n_2=\frac{139.5}{1.9}\approx 73.42$

Answer:

a) Approximately 27.37 packets
b) Approximately 73.42 packets