You go to a school dance. There is an entrance fee, and there are slices of pizza for sale. After having 1 slice of pizza, you have spent a total of $6. After having 2 more slices of pizza, you have spent a total of $10. Write an equation that represents the total cost y after buying x slices of pizza at the dance

Equation that represents the total cost is y = 4 + 2 x

Step-by-step explanation:

Here, x : slices of pizza eaten at the dance.

y : total cost paid in the school dance

Let a : Cost of each slice of pizza.

So, according to the question:

Entrance fee + cost 1 slice of pizza = $6

or, Entrance fee = $ 6 - Cost of 1 slice ... (1)

Similarly, Entrance fee + cost 3 slice of pizza = $10

or, Entrance fee = $ 10 - Cost of 3 slice ... (2)

Comparing both equation, we get:

$ 6 - Cost of 1 slice = $ 10 - Cost of 3 slice

or, 6 - a = 10 - 3 a

or, 2 a = 4

⇒ a = 2, So the cost of each slice of pizza = $2

Putting the value of a in 1 we get

Entrance fee = 6 - $ 2 = $4

Now, the cost of x slice of pizza = x ($2) = 2x

So, the total cost y for x slice of pizza = Entrance fee + Cost of x slices

or, y = $ 4 + 2 x

Equation that represents the total cost is y = 4 + 2 x