Comprehension
The following table presents the sweetness of different items relative to sucrose whose sweetness is taken to be 1.00.
| Item | Sweetness Relative to Sucrose |
|---|---|
| Lactose | 0.16 |
| Maltose | 0.32 |
| Glucose | 0.74 |
| Sucrose | 1.00 |
| Fructose | 1.70 |
| Saccharin | 675.00 |
Question: 1
What is the minimum amount of sucrose (to the nearest gram) that must be added to one gram of saccharin to make a mixture that will be at least 100 times as sweet as glucose?
What is the minimum amount of sucrose (to the nearest gram) that must be added to one gram of saccharin to make a mixture that will be at least 100 times as sweet as glucose?
Show Hint
For mixture problems, first calculate the total required sweetness and then solve for the unknown quantity based on the given sweetness values of the components.
Updated On: Mar 24, 2026
- 7
- 8
- 9
- 100
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The Correct Option is B
Solution and Explanation
We are given that the sweetness of glucose is 0.74, and saccharin has a sweetness of 675. The goal is to make the mixture 100 times as sweet as glucose. We use the equation:
\[
\text{Sweetness of mixture} = \text{Sweetness of sucrose} \times x + \text{Sweetness of saccharin} \times 1
\]
The required sweetness should be at least 100 times that of glucose, i.e., 74. By solving the equation for \( x \) (the amount of sucrose), we find the minimum amount of sucrose needed.
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Question: 2
Approximately how many times sweeter than sucrose is a mixture consisting of glucose, sucrose, fructose in the ratio 1: 2: 3?
Approximately how many times sweeter than sucrose is a mixture consisting of glucose, sucrose, fructose in the ratio 1: 2: 3?
Show Hint
When working with mixtures, use the weighted average to find the combined sweetness, then compare it to the sweetness of individual components.
Updated On: Aug 5, 2025
- 1.3
- 1
- 0.6
- 2.3
Show Solution
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The Correct Option is A
Solution and Explanation
We know the sweetness values:
- Glucose = 0.74
- Sucrose = 1.00
- Fructose = 1.70
To calculate the total sweetness of the mixture, use the given ratio of 1:2:3, and find the weighted average sweetness of the mixture:
\[
\text{Sweetness of mixture} = \frac{1(0.74) + 2(1.00) + 3(1.70)}{1 + 2 + 3}
\]
After calculating the total sweetness, compare it to the sweetness of sucrose to find the answer.
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