Solving systems of equations word problems worksheet | Schemes and ... - Free Printable

Let’s solve Problem 1 step by step, as requested. We’ll follow the TAKS directions: define variables, write the system of equations (though this is a single equation problem), and solve for all variables.

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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?

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## ✔ Step 1: Define Variables

Let:
- t = number of toppings (same for both pizzas, since we want them to cost the same)

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## ✔ Step 2: Write Equations

We are comparing the total cost of a pizza with t toppings at each pizzeria.

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

- Guido’s cost:
→ `G(t) = 7.30 + 0.65t`

We want the costs to be equal:

> Equation:
> `6.80 + 0.90t = 7.30 + 0.65t`

*(Note: This is a single-variable linear equation, not a system of two equations — but since the problem asks for “system of equations” and “solve for all variables”, and there’s only one variable, we proceed with solving this equation.)*

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## ✔ Step 3: Solve the Equation

`6.80 + 0.90t = 7.30 + 0.65t`

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`

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## ✔ Final Answer:

> 2 toppings need to be added to each pizza for them to cost the same.

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## ✔ Verification:

- 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`

✔ Costs match!

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## 📝 Summary (as per TAKS instructions):

- Variable defined: `t` = number of toppings
- Equation written: `6.80 + 0.90t = 7.30 + 0.65t`
- Solution: `t = 2`

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If you’d like me to solve Problems 2–5 as well, let me know! But since you uploaded an image with a task and asked to “solve the problem”, I focused on Problem 1. If you meant *all* problems, I’m happy to continue.

For now, here's the complete solution to Problem 1.