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;

●cups and liters,
●cups and pints,
●and pints and liters.

Show all your work and submit your work along with the resulting relationships.

Answer 1

Here's work you can copy and paste:

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

1Liter = 2.1 Cups

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

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

Answer 2

7 cups + 3 litres = 9.8 pints

`7c+3l=9.8p` ⇒ Equation 1

5 litres - 9 cups = 6 pints

`5l-9c=6p` ⇒ Equation 2

Relationship between cups and litres
Rearranging equation 1 to make pints the subject

`7c+3l=9.8p`

`p= (7c+3l)/(9.8)` ⇒ substitute this into Equation 2


`5l-9c= (7c+3l)/(9.8)`

`49l-88.2c=7c+3l`

`49l-3l=7c+88.2c`

`46l=95.2c`

`l=2.1c`

Hence, 1 litre = 2.1 cups

Relationship between cups and pints
Rearrange equation 1 to make litres the subject

`7c+3l=9.8p`

`3l=9.8p-7c`

`l= (9.8p-7c)/(3)` ⇒ Substituting this into Equation 2


`5( (9.8p-7c)/(3))-9c=6p`

`(49p-35c)/(3)-9c=6p`

`(49)/(3)p- (35)/(3)c-9c=6p`

`(49p)/(3)-6p= (35)/(3)+9c`

`(31)/(3)p= (62)/(3)c`

`p=2c`

Hence, 1 pint = 2 cups

Relationship between pints and litres
Rearranging equation 1 to make cup the subject


`7c=9.8p-3l`

`c= (9.8p-3l)/(7)` ⇒ subsitute this into equation 2


`5l-9( (9.8p-3l)/(7))=6p`

`5l- (63)/(5)p+ (27)/(7)l=6p`

`5l+ (27)/(7)l=6p+ (63)/(5)p`

`(62)/(7)l= (93)/(5)p`

`l=2.1p`

Hence, 1 litre = 2.1 pints