Question

a chemist working on a flu vaccine needs to mix a 20% sodium-iodine solution with a 30% sodium-iodine solution to obtain a 60-milliliter mixture. write the amount of sodium iodine in the mixture, s, in milliliters, as a function of the number of milliliters of the 20% solution used, x. then find and interpret s(40).
the amount of sodium iodine in the mixture, s, in milliliters, is s(x) = \boxed{ }, where x is the number of milliliters of the 20% solution.
(use integers or decimals for any numbers in the expression.)

Explanation:

Step1: Determine the amount of 30% solution

The total mixture is 60 milliliters, and the amount of the 20% solution is \( x \) milliliters. So, the amount of the 30% solution is \( 60 - x \) milliliters.

Step2: Calculate the sodium iodide from each solution

The amount of sodium iodide from the 20% solution is \( 0.20x \) milliliters (since 20% = 0.20). The amount from the 30% solution is \( 0.30(60 - x) \) milliliters (since 30% = 0.30).

Step3: Find the total sodium iodide \( S(x) \)

To find the total amount \( S(x) \), we add the two amounts together:

$$
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$$

Step4: Find \( S(40) \)

Substitute \( x = 40 \) into the function \( S(x) \):

$$
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$$

Answer:

The function is \( S(x) = -0.1x + 18 \) and \( S(40) = 14 \). The interpretation of \( S(40) = 14 \) is that when 40 milliliters of the 20% sodium - iodine solution is used (and thus \( 60 - 40=20 \) milliliters of the 30% solution is used), the total amount of sodium iodine in the 60 - milliliter mixture is 14 milliliters.