Question

The cost in dollars, y, of a large pizza with x toppings from Pat’s Pizzeria can be modeled by a linear function. A large pizza with no toppings costs $14.00. A large pizza with 2 toppings costs $17.50.

What is the cost of a pizza with 5 toppings? Round to the nearest penny.

Answer 1

Answer: $22.75

Explanation:

Given : The cost in dollars, y, of a large pizza with x toppings from Pat’s Pizzeria can be modeled by a linear function.

A linear function is given by :-

`y=mx+c` (1)

, where m is slope (rate of change of y w.r.t x) and c is the y-intercept.

A large pizza with no toppings costs $14.00.

i.e. for x=0 , y= 14

Put theses values in (1) , we get

`14=m(0)+c\\\Rightarrow\ c=14` (2)

A large pizza with 2 toppings costs $17.50.

i.e. for x=2 , y= 17.50

Put theses values in (1) , we get

`17.50=m(2)+c`

Put value of c from (2)

`17.50=2m+14\\\\`

Subtract 14 from both sides , we get

`3.50=2m`

Divide both sides by 2 , we get

`1.75=m`

Put m= 1.75 and c= 14 in (1) , the linear function representing cost of large pizza becomes
`y=1.75x+14`

At x= 5

`y=1.75(5)+14=8.75+14=22.75`

Thus , the cost of a pizza with 5 toppings= $22.75

Answer 2

$22.75

Start by finding the cost of each topping. Subtract $17.50 minus $14.00 to find that adding 2 toppings costs $3.50. Now, divide $3.50 by 2 to find that the cost for adding only one topping is $1.75.

Then, multiply $1.75 by 5 to find how much it costs to add 5 toppings. You get $8.75.

Finally, add the cost of 5 toppings to the cost of a large pizza with no toppings. $14.00 plus $8.75 equals $22.75, so a large pizza with 5 toppings costs $22.75.