Question

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?

• A. 7
• B. 8
• C. 9
• D. 100
• A. 1.3
• B. 1
• C. 0.6
• D. 2.3

Answer 1

The Correct Option is B

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.

Answer 2

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.