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. 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.Part 1: Write Miles' equation.(1 point)Responses 5j + 2p = 37.505j + 2p = 37.507x = 37.507x = 37.50j + p= 37.50j + p= 37.505j2p=37.50 5 j over 2 p is equal to 37 point 5 0Question 2Part 2: Write Emma's equation.(1 point)Responses 4j + 3p = 40.504j + 3p = 40.50j + p = 40.50j + p = 40.507x = 40.507x = 40.504j3p = 40.50

Question

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. 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.Part 1: Write Miles' equation.(1 point)Responses    5j + 2p = 37.505j + 2p = 37.507x = 37.507x = 37.50j + p= 37.50j + p= 37.505j2p=37.50    5 j over 2 p is equal to 37 point 5 0Question 2Part 2: Write Emma's equation.(1 point)Responses    4j + 3p = 40.504j + 3p = 40.50j + p = 40.50j + p = 40.507x = 40.507x = 40.504j3p = 40.50

GPT-4o mini · Answer

To set up the system of equations for Miles and Emma's purchases, let's define the variables:

Let $ j $ represent the cost of one jar of jam.
Let $ p $ represent the cost of one pie.

Part 1: Write Miles' equation.

Miles buys 5 jars of jam and 2 pies for a total of $37.50. This can be expressed as:

\[ 5j + 2p = 37.50 \]

Part 2: Write Emma's equation.

Emma buys 4 jars of jam and 3 pies for a total of $40.50. This can be expressed as:

\[ 4j + 3p = 40.50 \]

Thus, the system of equations is:

$ 5j + 2p = 37.50 $
$ 4j + 3p = 40.50 $