How does recipe conversion factors work? For example, if I have a soup that is originally 24 servings and has 16 oz of fish, and I need it to be done in 10 servings, what would the calculation be to get the right amount of fish.

You have to find the unit rate, which in this case means the amount of fish you need per serving of soup.

If 16 oz of fish makes 24 servings, then 16/24 oz = 2/3 oz makes 1 serving.

Now multiply both quantities by 10, so that 10 servings require 20/3 oz ≈ 6.67 oz of fish.

A more direct way to do this is to solve for x in the following equation:

(16 oz fish) / (24 servings) = (x oz fish) / (10 servings)

Then (omitting units)

x = 10 • 16 / 24 = 20/3

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.