Math Problem Statement
Tara makes donut topping by mixing sugar and [12,\text{g}] of cinnamon. The tape diagram shows the ratio of sugar to cinnamon. A tape diagram with 2 tapes of unequal lengths. The first tape has 3 equal parts. A curved bracket above the first tape is labeled Sugar. The second tape has 2 equal parts of the same size as in the first tape. A curved bracket below the second tape is labeled Cinnamon. Complete the table. Original ratio Amount ( [\text{g}]) Sugar [3] Cinnamon [12] Total topping [5]
Solution
Given the tape diagram and the information about the ratio of sugar to cinnamon, we can interpret and complete the table step by step.
The tape diagram shows:
- Sugar has 3 equal parts.
- Cinnamon has 2 equal parts. This gives a ratio of sugar to cinnamon of .
Now, we are told that of cinnamon corresponds to the 2 parts of cinnamon. Therefore, each part in the diagram represents:
Since sugar has 3 parts, the total amount of sugar will be:
Completing the table:
Original ratio | Amount (g) |
---|---|
Sugar | 18 |
Cinnamon | 12 |
Total topping |
The total topping is the sum of sugar and cinnamon, which is 30 grams.
Would you like further details or have any questions?
Here are 5 related questions to explore this further:
- What would be the amount of sugar if there were 24 grams of cinnamon?
- How would the total amount of topping change if the cinnamon amount were doubled?
- If Tara wanted to mix 45 grams of topping, how much sugar and cinnamon would she need?
- How can we express the ratio of sugar to the total topping in simplest form?
- What is the percentage of cinnamon in the total mixture?
Tip: Ratios can help scale recipes up or down while maintaining the same proportions between ingredients.
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Math Problem Analysis
Mathematical Concepts
Ratios
Proportions
Basic Arithmetic
Formulas
Ratio of sugar to cinnamon: 3:2
Amount per part of cinnamon: 12g / 2 = 6g
Amount of sugar: 3 parts * 6g = 18g
Total topping: 18g + 12g = 30g
Theorems
None
Suitable Grade Level
Grades 6-8
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