Your family signed up to bring collard greens and potato salad to this year’s Community Center Fall Fest & Potluck. You will need chicken broth for both recipes: 4 ⅔ cups for the collard greens and 3.75 cups to boil the potatoes.

Question

 
There is an open carton of chicken broth in the fridge with 1 ½ cups in it.  If there are 4 cups of chicken broth in one carton, how many cartons will you need to buy? How much chicken broth will be left over?

Answer 1

First, let's determine the total amount of chicken broth needed for both recipes.

For the collard greens, you need:

• 4 ⅔ cups

For the potato salad, you need:

• 3.75 cups

Now we convert these measurements to a common form:

• 4 ⅔ cups = \(4 + \frac{2}{3} = \frac{12}{3} + \frac{2}{3} = \frac{14}{3}\) cups
• 3.75 cups = \( \frac{15}{4} \) cups

Next, we will find a common denominator to add these two fractions. The least common multiple of 3 and 4 is 12.

Converting each measurement to twelfths:

• \( \frac{14}{3} \) cups: \[ \frac{14}{3} \times \frac{4}{4} = \frac{56}{12} \]
• \( \frac{15}{4} \) cups: \[ \frac{15}{4} \times \frac{3}{3} = \frac{45}{12} \]

Now we can add them: \[ \frac{56}{12} + \frac{45}{12} = \frac{101}{12} \text{ cups} \]

Now, we convert \( \frac{101}{12} \) cups to a mixed number: \[ \frac{101}{12} = 8 \frac{5}{12} \text{ cups} \]

Next, we need to determine how much chicken broth you already have. You have 1 ½ cups. Convert 1 ½ to a fraction: \[ 1 \frac{1}{2} = \frac{3}{2} \text{ cups} \]

To add it to the required amount in twelfths, we will convert \( \frac{3}{2} \) to twelfths: \[ \frac{3}{2} \times \frac{6}{6} = \frac{18}{12} \text{ cups} \]

Now we find how much more chicken broth you need: \[ \frac{101}{12} - \frac{18}{12} = \frac{83}{12} \text{ cups} \]

To find out how many cartons of broth you need to buy, we know there are 4 cups of broth in a carton: \[ \frac{83}{12} \div 4 = \frac{83}{12} \times \frac{1}{4} = \frac{83}{48} \]

To express this in mixed numbers: \[ \frac{83}{48} = 1 \frac{35}{48} \text{ cartons} \]

Since you can't buy a fraction of a carton, you will need to buy 2 cartons of chicken broth.

Now, let's find out how much chicken broth will be left over after you purchase 2 cartons. First, calculate how much broth you’ll have: \[ 2 \text{ cartons} \times 4 \text{ cups/carton} = 8 \text{ cups} \]

Now, total broth available after buying the cartons: \[ 8 \text{ cups} + 1.5 \text{ cups} = 8 + 1.5 = 9.5 \text{ cups} \]

Finally, calculate how much broth will be left over: \[ 9.5 \text{ cups} - \frac{101}{12} \text{ cups} = 9.5 - 8.4167 \approx 1.0833 \text{ cups} \]

Converting that back into a fraction gives about \(1 \frac{5}{12}\) cups remaining.

In conclusion:

• You will need to buy 2 cartons of chicken broth.
• There will be approximately 1 5/12 cups of chicken broth left over.