Algebra - Proportions | Practice Hub

To make 36 cookies, a recipe calls for 5 ounces of chocolate chips. How many ounces of chocolate chips would you need to make 900 cookies?

None of the other answers

Explanation

To figure out how many ounces of chocolate chips are needed to make 900 cookies, you simply need to set up a proportion. In this case, we know that 5 ounces of chocolate chips are needed to make 36 cookies, and we are trying to make a total of 900 cookies. Therefore, you can set up the proportion as

$\frac{5}{36}=\frac{x}{900}$

where is the ounces of chocolate chips needed to make 900 cookies.

For this proportion, solving for would give you a result of 125 ounces of chocolate chips.

If , what is the value of ?

Explanation

To solve this equation, we need to set up a simple proportion. Since the variables and are already in use, let's call the quantity that we are solving for . From the given information, we know we can use the proportion $\frac{9x}{17y} = \frac{24x}{z}$ . Cross-multiplication yields . Dividing by the common term of and simplifying the right side gives us , so our solution must be .

$\frac{x}{-3}=\frac{27}{-x}$

$\pm9$

$\pm81$

Explanation

To solve for , we just cross-multiply.

$\frac{x}{-3}=\frac{27}{-x}$

We have .

When multiplying a negative and positive number, our answer is negative.

We now have .

We can divide both sides by to get .

Take square root on both sides. Remember, when we do that the answer is $\pm \sqrt{81}$ . Two negative or two positive numbers multiplied can give us a positve value. is the answer to that perfect square and we add the positive and negative sign to get $\pm9$ .