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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.

Respuesta :

merlynthewhizz
7 cups + 3 litres = 9.8 pints 
[tex]7c+3l=9.8p[/tex] ⇒ Equation 1

5 litres - 9 cups = 6 pints
[tex]5l-9c=6p[/tex] ⇒ Equation 2

Relationship between cups and litres
Rearranging equation 1 to make pints the subject
[tex]7c+3l=9.8p[/tex]
[tex]p= \frac{7c+3l}{9.8} [/tex] ⇒ substitute this into Equation 2

[tex]5l-9c= \frac{7c+3l}{9.8} [/tex]
[tex]49l-88.2c=7c+3l[/tex]
[tex]49l-3l=7c+88.2c[/tex]
[tex]46l=95.2c[/tex]
[tex]l=2.1c[/tex]

Hence, 1 litre = 2.1 cups

Relationship between cups and pints
Rearrange equation 1 to make litres the subject
[tex]7c+3l=9.8p[/tex]
[tex]3l=9.8p-7c[/tex]
[tex]l= \frac{9.8p-7c}{3} [/tex] ⇒ Substituting this into Equation 2

[tex]5( \frac{9.8p-7c}{3})-9c=6p [/tex]
[tex] \frac{49p-35c}{3}-9c=6p [/tex]
[tex] \frac{49}{3}p- \frac{35}{3}c-9c=6p [/tex]
[tex] \frac{49p}{3}-6p= \frac{35}{3}+9c [/tex]
[tex] \frac{31}{3}p= \frac{62}{3}c [/tex]
[tex]p=2c[/tex]

Hence, 1 pint = 2 cups

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

[tex]7c=9.8p-3l[/tex]
[tex]c= \frac{9.8p-3l}{7} [/tex] ⇒ subsitute this into equation 2

[tex]5l-9( \frac{9.8p-3l}{7})=6p [/tex]
[tex]5l- \frac{63}{5}p+ \frac{27}{7}l=6p [/tex]
[tex]5l+ \frac{27}{7}l=6p+ \frac{63}{5}p [/tex]
[tex] \frac{62}{7}l= \frac{93}{5}p [/tex]
[tex]l=2.1p[/tex]

Hence, 1 litre = 2.1 pints


ambermcdowell1401

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

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