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.

Darian Hubbard

Darian Hubbard

Answered question

2022-07-20

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 & Explanation

repotasonwf

repotasonwf

Beginner2022-07-21Added 12 answers

7  cups + 3  litres  = 9.8  pints 
7 c + 3 l = 9.8 Equation 1
5  litres  9  cups  = 6  pints
5 l 9 c = 6 p Equation 2
Relationship between cups and litres
Rearranging equation 1 to make pints the subject
7 c + 3 l + 9.8 p
p = 7 c + 3 l 9.8 substitute this into Equation 2
5 l 9 c = 7 c + 3 l 9.8 49 l 88.2 c = 7 c + 3 l 49 l 3 l = 7 c + 88.2 c 46 l = 95.2 c l = 2.1 c
Hence, 1 litre = 2.1 cups
Relationship between cups and pints
Rearrange equation 1 to make litres the subject
7 c + 3 l = 9.8 3 l = 9.8 p 7 c l = 9.8 p 7 c 3 Substituting this into Equation 2
5 ( 9.8 p 7 c 3 ) 9 c = 6 p 49 p 35 c 3 9 c = 6 p 49 3 p 35 3 c 9 c = 6 p 49 p 3 6 p = 35 3 + 9 c 31 3 p = 62 3 c p = 2 c
Hence, 1 pint = 2 cups
Relationship between pints and litres
Rearranging equation 1 to make cup the subject
7 c = 9.8 3 l c = 9.8 p 3 l 7 subsitute this into equation 2
5 l 9 ( 9.8 p 3 l 7 ) = 6 p 5 l 63 5 p + 27 7 l = 6 p 5 l + 27 7 l = 6 p + 63 5 p 26 7 l = 93 5 p l = 2.1 p
Hence, 1 litre = 2.1 pints

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