Question

1. a store sells ice cream with assorted toppings. they charge $3.00 for an ice cream, plus $0.50 per ounce of toppings.

a. how much does an ice cream cost with 4 ounces of toppings?
b. how much does an ice cream cost with 11 ounces of toppings?
c. if elena’s ice cream costs $1.50 more than jada’s ice cream, how much more did elena’s toppings weigh?

Explanation:

Part a

Step1: Identify the cost formula

The base cost of ice cream is $3.00, and the cost per ounce of toppings is $0.50. So the total cost \( C \) for an ice cream with \( x \) ounces of toppings is \( C = 3 + 0.5x \).

Step2: Substitute \( x = 4 \) into the formula

Substitute \( x = 4 \) into \( C = 3 + 0.5x \), we get \( C = 3 + 0.5\times4 \).

Step3: Calculate the result

First, calculate \( 0.5\times4 = 2 \), then \( 3 + 2 = 5 \).

Step1: Use the same cost formula

The formula for total cost is still \( C = 3 + 0.5x \), where \( x \) is the number of ounces of toppings.

Step2: Substitute \( x = 11 \) into the formula

Substitute \( x = 11 \) into \( C = 3 + 0.5x \), we get \( C = 3 + 0.5\times11 \).

Step3: Calculate the result

First, calculate \( 0.5\times11 = 5.5 \), then \( 3 + 5.5 = 8.5 \).

Step1: Let Jada's topping weight be \( x \) and Elena's be \( y \)

Jada's cost \( C_J = 3 + 0.5x \), Elena's cost \( C_E = 3 + 0.5y \). We know that \( C_E - C_J = 1.50 \).

Step2: Substitute the cost formulas into the difference equation

Substitute \( C_J \) and \( C_E \) into \( C_E - C_J = 1.50 \), we get \( (3 + 0.5y) - (3 + 0.5x) = 1.50 \).

Step3: Simplify the equation

Simplify the left - hand side: \( 3 + 0.5y - 3 - 0.5x = 1.50 \), which simplifies to \( 0.5(y - x)=1.50 \).

Step4: Solve for \( y - x \)

Divide both sides of the equation \( 0.5(y - x)=1.50 \) by 0.5, we get \( y - x=\frac{1.50}{0.5}=3 \).

Answer:

The cost of an ice cream with 4 ounces of toppings is $5.00.

Part b