Question

a student is selling small and large frozen pizzas for a school fund - raiser.

• the student earns $3 for each small pizza sold.
• the student earns $4 for each large pizza sold.
• the student has sold exactly 30 pizzas.
• the student has earned $100.

how many small pizzas and large pizzas has the student sold?

1. 10 small pizzas, 20 large pizzas
2. 14 small pizzas, 16 large pizzas
3. 18 small pizzas, 12 large pizzas
4. 20 small pizzas, 10 large pizzas

Explanation:

Step1: Define variables

Let $x$ = number of small pizzas, $y$ = number of large pizzas.

Step2: Set up total pizza equation

Total pizzas sold: $x + y = 30$

Step3: Set up total earnings equation

Total earnings: $3x + 4y = 100$

Step4: Solve for one variable

From Step2: $x = 30 - y$

Step5: Substitute into earnings equation

$3(30 - y) + 4y = 100$
$90 - 3y + 4y = 100$
$90 + y = 100$
$y = 10$

Step6: Find number of small pizzas

$x = 30 - 10 = 20$

Answer:

1. 20 small pizzas, 10 large pizzas