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

To find the number of sugar - packets in a 12 - ounce can of Sunkist, divide the sugar content in Sunkist by the sugar content in one packet.
Let \(n_1\) be the number of sugar - packets in Sunkist. Given that a 12 - ounce can of Sunkist has 52 grams of sugar and a sugar packet has 1.9 grams of sugar. Then \(n_1=\frac{52}{1.9}\approx27.37\).

Step2: Calculate sugar content per ounce of Mt. Dew

First, find the sugar content per ounce of Mt. Dew. A 12 - ounce can of Mt. Dew has 46.5 grams of sugar. So the sugar content per ounce \(s=\frac{46.5}{12}=3.875\) grams per ounce.

Step3: Calculate total sugar in 2 Mt. Dews

The first Mt. Dew is 20 ounces and the second is 16 ounces. The total volume of Mt. Dew is \(V = 20 + 16=36\) ounces. The total sugar content \(S\) in 36 ounces of Mt. Dew is \(S=3.875\times36 = 139.5\) grams.

Step4: Calculate sugar - packets in 2 Mt. Dews

Let \(n_2\) be the number of sugar - packets in 2 Mt. Dews. Then \(n_2=\frac{139.5}{1.9}\approx73.42\).

Answer:

a) Approximately 27.37 packets
b) Approximately 73.42 packets