Question

The Chemistry Club is experimenting with different mixtures of water with a

certain chemical to make fake snow.

To make each mixture, the students start with some amount of water, and then add

1/7 of that amount of the chemical, and then 9 more grams of the chemical. The

chemical is expensive, so there can't be more than a certain number of grams of the

chemical in any one mixture. How much water can you start with so that you don't

use up too much of the chemical?

a. 1/7x + 9 < 26.25

b. 9x + 1/7 s 26.25

26.25x + 9 = 1/7

C.

d. 1/7x + 26.25 39

Answer 1

Suppose we have with x, the amount of water we use (in grams).

1/7 of this will be the chemical, then we have (1/7)*x grams of chemical.

Then we add another 9g of the chemical, then we have in total:

(1/7)*x + 9g of the chemical.

And we know that the chemical is expensive, so there can't be more than a given number of grams of the chemical, because of the phrase:

"...There can't be more than..."

We will have a relation like:

(1/7)*x + 9g ≤ something.

By looking at the options, we can see that "something" = 26.25 grams

then we will have the inequality:

(1/7)*x + 9g ≤ 26.25 g

Now we can solve this for x, the amount of water used:

(1/7)*x ≤ 26.25 g - 9g

x ≤ (26.25 g - 9g)*7

x ≤ 120.75 grams

This means that the maximum amount of water we can use is 120.75 grams of water.