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

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
$7c+3l=9.8p$
$p= \frac{7c+3l}{9.8}$ ⇒ substitute this into Equation 2

$5l-9c= \frac{7c+3l}{9.8}$
$49l-88.2c=7c+3l$
$49l-3l=7c+88.2c$
$46l=95.2c$
$l=2.1c$

Hence, 1 litre = 2.1 cups

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

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

Hence, 1 pint = 2 cups

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

$7c=9.8p-3l$
$c= \frac{9.8p-3l}{7}$ ⇒ subsitute this into equation 2

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

Hence, 1 litre = 2.1 pints