Question

osh and his friends bought vanilla wafers for $4 per packet and chocolate wafers for $1 per packet at a carnival. They spent a total of $45 to buy a total of 27 packets of wafers of the two varieties. Part A: Write a system of equations that can be solved to find the number of packets of vanilla wafers and the number of packets of chocolate wafers that Josh and his friends bought at the carnival. Define the variables used in the equations. (5 points) Part B: How many packets of chocolate wafers and vanilla wafers did they buy? Explain how you got the answer and why you selected a particular method to get the answer.

Answer 1

Let
x-----------> the number of packets of vanilla wafers-------> $4 per packet
y-----------> the number of packets of chocolate wafers -------> $1 per packet

we know that
x+y=27-------------> x=27-y----> equation 1
4x+y=45----------------------> equation 2

the answer part A) is 
the system of equations is
x+y=27
4x+y=45

Part B) 

I selected the  substitution method to get the answer to solve systems of two equations, for its simplicity. Basically, the substitution method consists of

1.   Clear an unknown in one of the equations (equation 1)

2.   In the other equation (equation 2) that we have not used, the same incognito is replaced by the value obtained in step 1.

3.   Clear the only unknown that remains. We obtain the numerical value of an unknown quantity.

4.   Replace the unknowns cleared in step 3 by their numerical value (also obtained in step 3) in the equation obtained in step 1.

5.   Operate to obtain the numerical value of the other unknown quantity.

I substitute equation (1) in equation (2)

4*(27-y)+y=45---------> 108-4y+y=45----------> 108-45=4y-y------> y=63/3
y=21
x=27-y----------> x=27-21----------> x=6

the answer Part B) is
the number of packets of vanilla wafers is 6
the number of packets of chocolate wafers is 21

Answer 2

Part A:
 First we define the variables:
 x = vanilla wafers
 y = chocolate wafers
 We write the system of equations associated with the problem:
 x + y = 27
 4x + y = 45
 Answer:
 x + y = 27
 4x + y = 45
 Part B:
 Since it is a system of two equations with two unknowns, it is convenient to use the graphical method to find the solution.
 The solution will be the intersection with both lines.
 For this case we obtain that the solution is:
 x = 6
 y = 21
 Answer:
 chocolate wafers = 21
 vanilla wafers = 6 
 Note: see attached image.