Questions: The table shows how much a fruit bar charges for their fruit cups. Write an expression to show how much it costs to buy a small cup of fruit with no toppings, and a large cup of fruit with x toppings. Then, find the total cost for a small cup of fruit with no toppings, and a large cup of fruit with 3 toppings. Write an expression for the total cost of a small cup of fruit with no toppings, and a large cup of fruit with x toppings.

The table shows how much a fruit bar charges for their fruit cups. Write an expression to show how much it costs to buy a small cup of fruit with no toppings, and a large cup of fruit with x toppings. Then, find the total cost for a small cup of fruit with no toppings, and a large cup of fruit with 3 toppings.

Write an expression for the total cost of a small cup of fruit with no toppings, and a large cup of fruit with x toppings.

Transcript text: The table shows how much a fruit bar charges for their fruit cups. Write an expression to show how much it costs to buy a small cup of fruit with no toppings, and a large cup of fruit with $x$ toppings. Then, find the total cost for a small cup of fruit with no toppings, and a large cup of fruit with 3 toppings. Write an expression for the total cost of a small cup of fruit with no toppings, and a large cup of fruit with $\times$ toppings.

Solution

Solution Steps

To solve this problem, we need to create expressions for the cost of a small cup of fruit with no toppings and a large cup of fruit with $ x $ toppings. The cost of a small cup is given directly, while the cost of a large cup with toppings involves adding the base cost of the large cup to the cost of the toppings. Finally, we calculate the total cost for a small cup with no toppings and a large cup with 3 toppings by substituting $ x = 3 $ into the expression for the large cup.

Step 1: Define the Costs

The cost of a small cup of fruit is given as $ C_{\text{small}} = 2.75 $. The cost of a large cup of fruit is $ C_{\text{large}} = 4.25 $, and the cost per topping for the large cup is $ C_{\text{topping}} = 0.30 $.

Step 2: Write the Expression for Total Cost

The total cost $ C_{\text{total}} $ for a small cup with no toppings and a large cup with $ x $ toppings can be expressed as: \[ C_{\text{total}} = C_{\text{small}} + (C_{\text{large}} + x \cdot C_{\text{topping}}) \]

Step 3: Substitute for Specific Values

For the specific case of a large cup with 3 toppings ($ x = 3 $): \[ C_{\text{total}} = 2.75 + (4.25 + 3 \cdot 0.30) \]

Step 4: Calculate the Total Cost

Calculating the cost of the large cup with 3 toppings: \[ C_{\text{total}} = 2.75 + (4.25 + 0.90) = 2.75 + 5.15 = 7.90 \]