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At a country fair, 4 burgers and 2 orders of French fries cost $20.00, while 2 burgers and 3 orders of French fries cost $14.00. Write and solve a system of equations to find the cost of a single burger and an order of French fries.

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Final answer:

To solve this problem, set up a system of equations and solve using substitution or elimination. The cost of a single burger is $4.00 and the cost of an order of French fries is $2.00.

Step-by-step explanation:

To solve this problem, we can set up a system of equations based on the information given. Let's define the cost of a burger as 'x' and the cost of an order of French fries as 'y'.

From the first scenario, we know that 4 burgers and 2 orders of French fries cost $20.00. This can be written as the equation 4x + 2y = 20.

From the second scenario, we know that 2 burgers and 3 orders of French fries cost $14.00. This can be written as the equation 2x + 3y = 14.

We now have a system of equations:

4x + 2y = 20

2x + 3y = 14

We can solve this system by using the method of substitution or elimination. Let's use the method of elimination:

Multiplying the first equation by 3, and the second equation by 2, we get:

12x + 6y = 60

4x + 6y = 28

Now, subtracting the second equation from the first equation, we eliminate 'y':

12x + 6y - (4x + 6y) = 60 - 28

8x = 32

Dividing both sides of the equation by 8, we find:

x = 4

Substituting the value of 'x' into the first equation, we can find the value of 'y':

4(4) + 2y = 20

16 + 2y = 20

Subtracting 16 from both sides of the equation, we find:

2y = 4

Dividing both sides of the equation by 2, we get:

y = 2

Therefore, the cost of a single burger is $4.00 and the cost of an order of French fries is $2.00.

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