# 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.

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.
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$7c+3l=9.8⇒$ Equation 1

$5l-9c=6p⇒$ Equation 2
Relationship between cups and litres
Rearranging equation 1 to make pints the subject
$7c+3l+9.8p$
$p=\frac{7c+3l}{9.8}⇒$ substitute this into Equation 2
$5l-9c=\frac{7c+3l}{9.8}\phantom{\rule{0ex}{0ex}}49l-88.2c=7c+3l\phantom{\rule{0ex}{0ex}}49l-3l=7c+88.2c\phantom{\rule{0ex}{0ex}}46l=95.2c\phantom{\rule{0ex}{0ex}}l=2.1c$
Hence, 1 litre = 2.1 cups
Relationship between cups and pints
Rearrange equation 1 to make litres the subject
$7c+3l=9.8\phantom{\rule{0ex}{0ex}}3l=9.8p-7c\phantom{\rule{0ex}{0ex}}l=\frac{9.8p-7c}{3}⇒$ Substituting this into Equation 2
$5\left(\frac{9.8p-7c}{3}\right)-9c=6p\phantom{\rule{0ex}{0ex}}\frac{49p-35c}{3}-9c=6p\phantom{\rule{0ex}{0ex}}\frac{49}{3}p-\frac{35}{3}c-9c=6p\phantom{\rule{0ex}{0ex}}\frac{49p}{3}-6p=\frac{35}{3}+9c\phantom{\rule{0ex}{0ex}}\frac{31}{3}p=\frac{62}{3}c\phantom{\rule{0ex}{0ex}}p=2c$
Hence, 1 pint = 2 cups
Relationship between pints and litres
Rearranging equation 1 to make cup the subject
$7c=9.8-3l\phantom{\rule{0ex}{0ex}}c=\frac{9.8p-3l}{7}⇒$ subsitute this into equation 2
$5l-9\left(\frac{9.8p-3l}{7}\right)=6p\phantom{\rule{0ex}{0ex}}5l-\frac{63}{5}p+\frac{27}{7}l=6p\phantom{\rule{0ex}{0ex}}5l+\frac{27}{7}l=6p+\frac{63}{5}p\phantom{\rule{0ex}{0ex}}\frac{26}{7}l=\frac{93}{5}p\phantom{\rule{0ex}{0ex}}l=2.1p$
Hence, 1 litre = 2.1 pints