Math Problem Statement

Emily needs 60g of fruit and 100ml of juice to make a small smoothie. She follows the same recipe to make a large smoothie. A large smoothie uses 350ml of juice. How much fruit will she need?

Solution

Let's break down the problem and verify the answer.

Given:

  • A small smoothie requires 60 g of fruit and 100 ml of juice.
  • A large smoothie uses 350 ml of juice.
  • We need to determine how much fruit is required for the large smoothie.

Step 1: Find the Scaling Factor

Since the small smoothie uses 100 ml of juice, and the large smoothie uses 350 ml, the scaling factor is:

350100=3.5\frac{350}{100} = 3.5

Step 2: Calculate the Fruit Requirement

Since the amount of fruit scales the same way, multiply the fruit amount by 3.5:

60×3.5=210 g60 \times 3.5 = 210 \text{ g}

Answer:

Emily will need 210 g of fruit.


Would you like a more detailed explanation or have any questions?

Here are 5 related questions for further practice:

  1. If Emily made a smoothie using 500 ml of juice, how much fruit would she need?
  2. If she only had 180 g of fruit, how much juice should she use to maintain the proportion?
  3. What is the ratio of fruit to juice in the original small smoothie?
  4. If a different smoothie recipe requires 80 g of fruit for 120 ml of juice, how much fruit is needed for 360 ml?
  5. If Emily wants to make half of a large smoothie, how much fruit and juice should she use?

Tip:

When scaling a recipe or ratio, always use proportional multiplication to ensure accurate results.

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Math Problem Analysis

Mathematical Concepts

Scaling
Ratios
Proportions

Formulas

Scaling Factor = (Large Quantity) / (Small Quantity)
Fruit Needed = Fruit in Small Smoothie × Scaling Factor

Theorems

Basic Proportions

Suitable Grade Level

Grades 5-7