Miles and Emma are buying jam and pies at a farm stand. Mrs. Moore sells all jars of jam for the same price. She also sells all of her pies for the same price. She also sells all of her pies for the same price. Miles pays 37.50 for 5 jars of jam and 2 pies. Emma pays 40.50 for 4 jars of jam and 3 pies. Write a system of equations that can be used to determine the cost of one jar of jam and the cost of one pie.
1 answer
Let \( j \) represent the cost of one jar of jam and \( p \) represent the cost of one pie. We can formulate the following two equations based on the purchases made by Miles and Emma.
From Miles' purchase, we have: \[ 5j + 2p = 37.50 \]
From Emma's purchase, we have: \[ 4j + 3p = 40.50 \]
Thus, the system of equations is: \[ \begin{cases} 5j + 2p = 37.50 \ 4j + 3p = 40.50 \end{cases} \]
