Question

Josh 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. (5 points)

Answer 1

x+y= 27   (we do not know how much of each) {First Equation}
4x+1y = 45 {Second Equation}

subtract x+y=27 from 4x+1y=45 if doing elimination.
(You could do it by either elimination or substitution to get )-----
x=6 that is the number of vanilla wafers.
and y =21 that is the number of Chocolate wafers. 
If you need further help, please let me know.....

Answer 2

Answer with explanation:

• Let x denotes the number of packets of vanilla wafers.

• and y denotes the number of packets of chocolate wafers.

Vanilla wafers cost $4 per packet

and chocolate wafers for $1 per packet

They spent a total of $45 .

This means that the equation that can be formed using this information is:

                   4x+y=45

and they buy a total of 27 packets of wafers.

i.e.   the equation formed with the help of this information is:

              x+y=27

PART A:

The 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 is:

                 4x+y=45-------------------(1)

and             x+y=27----------------(2)

PART B:

We will use the method of substitution because with the help of this method we could easily substitute the value of one variable in terms of the other variable and obtain the answer.

Using equation (2) we have:

   y=27-x-------------------(3)

On putting this value of y in equation (1) we have:

4x+27-x=45

i.e.

4x-x+27=45

i.e.

3x+27=45

i.e.

3x=45-27

i.e.

3x=18

i.e.

x=6

and on putting the value of x in equation (3) we have:

y=27-6

i.e.   y=21

Hence, number of vanilla wafers purchased = 6

and number of chocolates wafers purchased = 21