Worksheet featuring five word problems that require solving systems of equations, covering topics such as pizza toppings, CD sales, rectangle dimensions, food costs, and ice cream shop revenue.

Let’s solve Problem 1 step by step.

---

Problem 1:

> A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping.
> The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping.
> How many toppings need to be added to a large cheese pizza from Palanzio’s Pizzeria and Guido’s Pizza in order for the pizzas to cost the same, not including tax?

---

Step 1: Define variables

Let t = number of toppings on each pizza (we’re assuming both pizzas have the same number of toppings — that’s what “in order for the pizzas to cost the same” implies).

We want to find t such that:

Cost at Palanzio’s = Cost at Guido’s

---

Step 2: Write equations

Palanzio’s cost:
Base price + per topping × number of toppings →
P(t) = 6.80 + 0.90t

Guido’s cost:
Base price + per topping × number of toppings →
G(t) = 7.30 + 0.65t

Set them equal:

6.80 + 0.90t = 7.30 + 0.65t

---

Step 3: Solve the equation

Subtract 0.65t from both sides:

→ 6.80 + 0.25t = 7.30

Subtract 6.80 from both sides:

→ 0.25t = 0.50

Divide both sides by 0.25:

→ t = 0.50 / 0.25 = 2

---

Step 4: Check your answer

Plug t = 2 back into both original equations.

Palanzio’s: 6.80 + 0.90×2 = 6.80 + 1.80 = $8.60

Guido’s: 7.30 + 0.65×2 = 7.30 + 1.30 = $8.60

✔ They match! So 2 toppings make the prices equal.

---

Final Answer:
2