Kevin uses 84 fluid ounces of water to make an all-purpose cleaner. the directions call for 4 fluid ounces of concentrated soap for every 3 cups of water. how many fluid ounces of soap should he use? ( 1 cup = 8 fl oz

using unit rates to convert measurement

He should use 14 fluid ounces of soap.

Step-by-step explanation:

1. The first step is to make the conversion from cups to ounces. Knowing that:

You get:

2. According to the information given in the exercise, Kevin must use 4 fluid ounces of concentrated soap for every 3 cups of water or 24 fluid ounces of water.

Then, knowing that he uses 84 fluid ounces of water to make an all-purpose cleaner, you can set up the following proportion:

Where "x" is the total fluid ounces of soap that he should use.

3. Solving for "x", you get this result:

linearly: 8560 bacteria

exponentially: approximately 75233 bacteria

step-by-step explanation:

assuming it is not exponential (we would have some really complicated logarithms), let's say it is linear. then, after 5 hours, it increased by 1200 bacteria, so every hour it increases by 240 bacteria. this means that after 19 hours, we get 19 * 240 + 4000 bacteria or 3800 + 760 + 4000 = 7800 + 760 = 8560 bacteria.

because it says round your answer, i will do this exponentially (with a calculator, of course). first, we need to find how much it multiplies by every hour, by taking the 5th root of 52/40 or 13/10. this is approximately 0.167. we still need to add 1 to this, because we are multiplying by that number, not adding that amount of the number. now, we just calculate 4000 * (1.167)^19. use a calculator to get approximately 75232.6, or 75233.