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.​

Answer 1

The system of equations that can be solved to find the number of vanilla and chocolate wafers are

$4x+y=45\\x+y=27$

Given:

The cost of vanilla wafers = 4

The cost of chocolate wafers = 1

Total cost = 45

Total number of wafers = 27

To Find:

System of equations to find the number of packets

Solution:

• Let the number of packets of vanilla wafers be x.
• Let the number of packets of chocolate wafers be y.
• Therefore cost of vanilla wafers = 4x
• The cost of chocolate wafer s = y
• Total cost $= 4x+y=45$
• Total number of packets $= x+y=27$

Therefore the system of equations are

$4x+y=45\\x+y=27$

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Answer 2

Given data is

• Josh and his friends bought vanilla wafers for 4 dollars per packet and chocolate wafers for 1 dollar per packet.
• They spent 45 dollars to buy a total of 27 packets of wafers of two varieties.

Now, we need to convert this data into system of equations that can be solved to find the number of packets of vanilla wafers and chocolate wafers.

As, per the given question if we solve the equations we should get the number of vanilla wafers and number of chocolate wafers. Hence, the variables used in the equation should be the number of vanilla wafers and chocolate wafers.

Let, the number of vanilla wafers be

$x$

Let the number of chocolate wafers be

$y$

Now, the first equation can be obtained by the relation of money spent on wafers.

Josh and his friends spent a total of 45 dollars for wafers in which vanilla wafers are of 4 dollars for each packet and chocolate wafers are of 1 dollar for each packet.

This can be converted into a equation as follows

$4x + 1y = 45$

Now, the second equation can be obtained by the relation of number of wafers they bought.

Josh and their friends bought 27 wafers of two both the varieties of vanilla and chocolate.

This can be represented as

$x + y = 27$

Therefore, the equations are

$4x + 1y = 45 \\ x + y = 27$

In which x represents the number of vanilla wafers and y represents the number of chocolate wafers

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