Let's solve each problem step by step, identifying the
independent and
dependent variables, writing an equation, and then using the equation to find the requested values.
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Problem 1: David is going out for a pizza
Given:
- Base cost of pizza = $10.50
- Each extra topping costs $1.50
- Let *x* = number of extra toppings
- Total cost = ?
#### Step 1: Identify Variables
-
Independent variable: The quantity that you can choose or control.
→ Number of extra toppings (
x)
-
Dependent variable: The outcome that depends on the independent variable.
→ Total cost of the pizza (
y)
#### Step 2: Write the Equation
Total cost = Base price + (Cost per topping × Number of toppings)
So:
>
y = 10.50 + 1.50x
#### Step 3: Use the equation to find the total cost with 3 extra toppings
Plug in
x = 3:
> y = 10.50 + 1.50(3)
> y = 10.50 + 4.50
> y =
$15.00
✔ The total cost of the pizza is $15.00
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Problem 2: Alex is going on a road trip
Given:
- Speed = 65 miles per hour
- Time = h hours
- Distance = d miles
#### Step 1: Identify Variables
-
Independent variable: Time (h), because Alex chooses how long to drive
-
Dependent variable: Distance (d), which depends on time
#### Step 2: Write the Equation
Use the formula:
> Distance = Rate × Time
So:
>
d = 65h
#### Step 3: Find distance traveled in 8 hours
Plug in
h = 8:
> d = 65 × 8
> d =
520 miles
✔ The distance Alex would drive is 520 miles
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✔ Final Answers:
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Problem 1:
-
Independent variable: Number of extra toppings (x)
-
Dependent variable: Total cost of the pizza (y)
-
Equation: y = 10.50 + 1.50x
-
Total cost with 3 toppings: $15.00
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Problem 2:
-
Independent variable: Time (h)
-
Dependent variable: Distance (d)
-
Equation: d = 65h
-
Distance in 8 hours: 520 miles
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Let me know if you'd like this formatted as a completed worksheet!
Parent Tip: Review the logic above to help your child master the concept of independent dependent variable worksheet.
