Question

Jason is ordering pizzas for a school party.

Pizzeria A charges a flat delivery fee of $20 and $12 per pizza.

Pizzeria B charges a flat delivery fee of $8 and $15 per pizza.

Which of the following inequalities represents the number of pizzas, n, Jason must order so that Pizzeria A is the cheaper option?

Responses
A
n is less than 4
B
n is greater than 4
C
n is less than 12
D

Answer 1

To find the inequality that represents when Pizzeria A is cheaper than Pizzeria B, we can set up expressions for the total cost from each pizzeria.

Let's represent the total cost from Pizzeria A as:
\[ \text{Cost}_{A} = 20 + 12n \]

And the total cost from Pizzeria B as:
\[ \text{Cost}_{B} = 8 + 15n \]

We want to find when Pizzeria A is cheaper than Pizzeria B:
\[ 20 + 12n < 8 + 15n \]

Now, let's solve the inequality:

1. Subtract \(12n\) from both sides:
\[ 20 < 8 + 3n \]

2. Subtract 8 from both sides:
\[ 12 < 3n \]

3. Divide both sides by 3:
\[ 4 < n \]
Or, equivalently:
\[ n > 4 \]

Therefore, the correct inequality is:
**B: n is greater than 4**.