Let’s solve Problem 1 step by step.
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Step 1: Define variables
We are trying to find how many toppings make the two pizzas cost the same.
Let:
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t = number of toppings added to each pizza (same for both)
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Step 2: Write equations for total cost
For Palanzio’s Pizzeria:
- Base cost: $6.80
- Cost per topping: $0.90
→ Total cost = 6.80 + 0.90t
For Guido’s Pizza:
- Base cost: $7.30
- Cost per topping: $0.65
→ Total cost = 7.30 + 0.65t
We want these costs to be equal:
Equation:
6.80 + 0.90t = 7.30 + 0.65t
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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
t = 2
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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.
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Final Answer:
2
Parent Tip: Review the logic above to help your child master the concept of system of equations 3 variables worksheet.
