Question

A chemist working on a flu vaccine needs to mix a 20% sodium-iodine with a 60% sodium to obtain a 70-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(50)

Answer 1

To find the amount of sodium iodine in the mixture, we set up an equation using the given information and solve for x.To find S(50), we substitute 50 for x in the equation. The amount of sodium iodine in the mixture, S, is 62 milliliters.

Step-by-step explanation:

To find the amount of sodium iodine in the mixture, we can set up a equation based on the given information.

Let x be the number of milliliters of the 20% solution used.

To mix a 70-milliliter mixture, we would have 70 - x milliliters of the 60% solution.

Now, we can create an equation:

0.20x + 0.60(70 - x) = S

Simplifying the equation, we get:

0.20x + 42 - 0.60x = S

Combining like terms, we have:

0.40x + 42 = S

To find S(50), we substitute 50 for x in the equation:

0.40(50) + 42 = S(50)

Simplifying, we get:

20 + 42 = S(50)

S = 62 milliliters

Answer 2

`S(x)=-0.4x+42`

The value of S(50) is 22 in means the amount of sodium iodine in the mixture is 22 when 50 milliliters of the 20% solution used.

Step-by-step explanation:

It is given that a chemist working on a flu vaccine needs to mix a 20% sodium-iodine with a 60% sodium-iodine to obtain a 70-milliliter mixture.

Let x be the number of milliliters of the 20% sodium-iodine.

Number of milliliters of the 60% sodium-iodine = 70-x

The amount of sodium iodine in the mixture is 20% of x and 60% of (70-x).

`S(x)=0.20x+0.60(70-x)`

`S(x)=0.2x+42-0.6x`

`S(x)=-0.4x+42`

Therefore,the required function is
`S(x)=-0.4x+42`.

Substitute x=50 in the above equation.

`S(50)=-0.4(50)+42`

`S(50)=22`

The value of S(50) is 22 in means the amount of sodium iodine in the mixture is 22 when 50 milliliters of the 20% solution used.