Math Problem Statement

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

Solution

Let's solve the problem step by step.

Given information:

  • A small smoothie requires 60 g of fruit and 100 ml of juice.
  • A large smoothie uses 350 ml of juice.
  • The ratio of fruit to juice remains the same.

Step 1: Find the scaling factor

Since a small smoothie uses 100 ml of juice, and a large smoothie uses 350 ml, the scaling factor is: 350100=3.5\frac{350}{100} = 3.5

Step 2: Scale the fruit amount

Since fruit scales the same way: 60×3.5=210 g60 \times 3.5 = 210 \text{ g}

Final Answer:

Emily will need 210 g of fruit.

Would you like more clarification or details on any part?

Related Questions:

  1. What is the ratio of fruit to juice in a small smoothie?
  2. How much fruit would be needed for a smoothie with 500 ml of juice?
  3. If Emily makes 5 large smoothies, how much fruit will she need?
  4. How much juice is required for a smoothie using 150 g of fruit?
  5. Can you express the proportion of fruit to juice as a percentage?

Tip:

When solving proportion problems, always check that both quantities scale by the same factor.

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Math Problem Analysis

Mathematical Concepts

Proportions
Scaling
Ratios

Formulas

Scaling factor = (new quantity) / (original quantity)
Scaled value = original value × scaling factor

Theorems

Proportionality theorem

Suitable Grade Level

Grades 5-7