Answer :
Sure! Let's solve the problem step by step.
You have [tex]\(15 \frac{1}{4}\)[/tex] liters of soup in total, and you want to pour it into cups, each with a capacity of [tex]\(\frac{1}{5}\)[/tex] of a liter.
### A. How many cups can be filled with soup?
1. Convert the mixed number to an improper fraction:
[tex]\(15 \frac{1}{4}\)[/tex] liters is the same as 15 whole liters and [tex]\(\frac{1}{4}\)[/tex] of a liter.
To convert [tex]\(15 \frac{1}{4}\)[/tex] into an improper fraction:
[tex]\[
15 \frac{1}{4} = 15 + \frac{1}{4} = \frac{60}{4} + \frac{1}{4} = \frac{61}{4}
\][/tex]
So, you have [tex]\(\frac{61}{4}\)[/tex] liters of soup.
2. Determine how many [tex]\(\frac{1}{5}\)[/tex] liter cups can be filled:
To find out how many full cups of [tex]\(\frac{1}{5}\)[/tex] liter can be filled, divide the total liters by the capacity of one cup:
[tex]\[
\frac{61}{4} \div \frac{1}{5} = \frac{61}{4} \times \frac{5}{1} = \frac{61 \times 5}{4} = \frac{305}{4}
\][/tex]
[tex]\(\frac{305}{4}\)[/tex] can be calculated as a mixed number to find the number of whole cups.
[tex]\[
\frac{305}{4} = 76 \text{ whole cups} \quad \text{(Since 305 divided by 4 equals 76 with a remainder)}
\][/tex]
So you can fill 76 cups of soup.
### B. How much soup remains unserved?
1. Calculate the total liters of soup used in 76 cups:
Multiply the number of cups by the capacity of each cup to get the total liters used:
[tex]\[
76 \times \frac{1}{5} = \frac{76}{5} = 15.2 \text{ liters}
\][/tex]
2. Subtract the used soup from the total soup:
[tex]\[
\text{Total soup left} = 15 \frac{1}{4} - 15.2
\][/tex]
First, convert [tex]\(15 \frac{1}{4}\)[/tex] to decimal for easier calculation:
[tex]\[
15 \frac{1}{4} = 15.25 \text{ liters}
\][/tex]
Then subtract:
[tex]\[
15.25 - 15.2 = 0.05 \text{ liters} \quad \text{(rounded to two decimal places)}
\][/tex]
So, about 0.05 liters of soup remains unserved.
To summarize:
- You can fill 76 cups of soup.
- 0.05 liters of soup will be left unserved.
You have [tex]\(15 \frac{1}{4}\)[/tex] liters of soup in total, and you want to pour it into cups, each with a capacity of [tex]\(\frac{1}{5}\)[/tex] of a liter.
### A. How many cups can be filled with soup?
1. Convert the mixed number to an improper fraction:
[tex]\(15 \frac{1}{4}\)[/tex] liters is the same as 15 whole liters and [tex]\(\frac{1}{4}\)[/tex] of a liter.
To convert [tex]\(15 \frac{1}{4}\)[/tex] into an improper fraction:
[tex]\[
15 \frac{1}{4} = 15 + \frac{1}{4} = \frac{60}{4} + \frac{1}{4} = \frac{61}{4}
\][/tex]
So, you have [tex]\(\frac{61}{4}\)[/tex] liters of soup.
2. Determine how many [tex]\(\frac{1}{5}\)[/tex] liter cups can be filled:
To find out how many full cups of [tex]\(\frac{1}{5}\)[/tex] liter can be filled, divide the total liters by the capacity of one cup:
[tex]\[
\frac{61}{4} \div \frac{1}{5} = \frac{61}{4} \times \frac{5}{1} = \frac{61 \times 5}{4} = \frac{305}{4}
\][/tex]
[tex]\(\frac{305}{4}\)[/tex] can be calculated as a mixed number to find the number of whole cups.
[tex]\[
\frac{305}{4} = 76 \text{ whole cups} \quad \text{(Since 305 divided by 4 equals 76 with a remainder)}
\][/tex]
So you can fill 76 cups of soup.
### B. How much soup remains unserved?
1. Calculate the total liters of soup used in 76 cups:
Multiply the number of cups by the capacity of each cup to get the total liters used:
[tex]\[
76 \times \frac{1}{5} = \frac{76}{5} = 15.2 \text{ liters}
\][/tex]
2. Subtract the used soup from the total soup:
[tex]\[
\text{Total soup left} = 15 \frac{1}{4} - 15.2
\][/tex]
First, convert [tex]\(15 \frac{1}{4}\)[/tex] to decimal for easier calculation:
[tex]\[
15 \frac{1}{4} = 15.25 \text{ liters}
\][/tex]
Then subtract:
[tex]\[
15.25 - 15.2 = 0.05 \text{ liters} \quad \text{(rounded to two decimal places)}
\][/tex]
So, about 0.05 liters of soup remains unserved.
To summarize:
- You can fill 76 cups of soup.
- 0.05 liters of soup will be left unserved.
