Math Problem Statement

(01.03)

Laura is baking a cake. The recipe says that she has to mix 64 grams of chocolate powder to the flour. Laura knows that 1 cup of that particular chocolate powder has a mass of 128 grams. She added two over three of a cup of chocolate powder to the flour. Should Laura add more chocolate powder to make the exact recipe, or did she go over and by what amount? (1 point)

She went over by one over three of a cup

She needs to add one over three of a cup

She needs to add one over six of a cup

She went over by one over six of a cup

Solution

Let's break down the problem:

  1. The recipe requires 64 grams of chocolate powder.
  2. Laura knows that 1 cup of the chocolate powder weighs 128 grams.
  3. Laura added 23\frac{2}{3} of a cup.

Now, let's calculate how much chocolate powder Laura added:

  • 23\frac{2}{3} of 1 cup weighs 23×128=256385.33\frac{2}{3} \times 128 = \frac{256}{3} \approx 85.33 grams.

Next, compare this amount to the 64 grams the recipe requires:

  • Laura added approximately 85.33 grams, but the recipe only calls for 64 grams.
  • Therefore, she added more than the recipe requires.

Now, let's find by how much she went over:

  • 85.3364=21.3385.33 - 64 = 21.33 grams extra.

To convert this extra amount into cups, recall that 1 cup is 128 grams:

  • 21.3312816\frac{21.33}{128} \approx \frac{1}{6} of a cup.

So, Laura went over by 16\frac{1}{6} of a cup.

Correct Answer: She went over by one over six of a cup.


Do you want more details or have any questions?

Here are 5 related questions:

  1. How much chocolate powder is in 14\frac{1}{4} of a cup?
  2. If the recipe called for 96 grams of chocolate, how much would Laura need to add?
  3. What fraction of a cup should Laura have added to use exactly 64 grams of chocolate?
  4. If Laura added 12\frac{1}{2} of a cup, would she need to add more powder?
  5. How would the calculations change if the cup measured 150 grams instead?

Tip: Always verify units when working with weights and volumes to ensure accurate measurements in cooking.

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Math Problem Analysis

Mathematical Concepts

Ratios
Proportions
Unit Conversion

Formulas

Weight of chocolate added = (2/3) * 128 grams
Excess chocolate = Weight of chocolate added - 64 grams
Convert excess to cups = Excess chocolate / 128 grams per cup

Theorems

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Suitable Grade Level

Grades 6-8