Question

Melissa and Emily are playing at the pool.They have three different measuring jars for; liters, cups, and pints. They find that 7 cups of water and 3 liters of water filled 9.8 pints. Later, they find that if they start with 5 liters of water and remove 9 cups of water, they end up with 6 pints of water. Model the given two situations as a system of linear equations. Based on your equations, determine the relationship between;

Answer 1

Here is the missing part.

Cups and liters:-1 litre = 2.1 cups

Cups and pints:- 1 pint = 2 cups

Pints and liters:-1 litre = 2.1 pints

Explanation:

Step 1:

7 cups + 3 liters = 9.8 pints

`7c+3l=9.8p`

5 liters - 9 cups = 6 pints

`5l+9c=6p`

Cups and Liters

`7c+3l=9.8p`

`p= 7c+3l/9.8` (put in equation 2)

`5l-9c= 7c+3l/9.8\\49l-88.2c=7c+3l\\49l-3l=7c-88.2c\\46l=45.2c`

1 Liter = 2.1 Cups.

Step 2:

Cups and Pints

`7c+3l=9.8p\\3l=9.8p-7c`

`l=9.8p-7c/3`(put in equation 2)

`5(9.8p-7c/3)-9c=6p\\(49p-35c/3)-9c=6p\\49/3p-35/3c-9c=6p\\49/3p-6p=35/3c+9c\\31/3p=62/3c`

1 Pint = 2 Cups.

Step 3:

Pints and Liters

`7c=9.8p-3l`

`c=9.8p-3l/7`(put in equation 2)

`5l-9(9.8p-3l/7)=6p\\5l-63/5p+27/7l=6p\\5l+27/7l=6p+63/5p\\62/7l=93/5p`

​1 Liter = 2.1 Pints.