If the chance an event will happen is 3/11, that means there are 8 instances where the even would not occur out of every 11, giving us 8/11.

3 chances out of 11 = event

11 – 3 = 8

8 chances out of 11 = no event

Cross multiply:

$\displaystyle \small 7x\ =\ 4\times 28\ =112$

Solve for $\displaystyle x$:

$\displaystyle \small 7x\ =\ 112$

$\displaystyle \frac{112}{7}=16$

Use cross-multiplication to set up the following equation:

$\displaystyle \small \frac{n}{4\frac{1}{2}} = \frac{4\frac{2}{3}}{2\frac{1}{4}}$ 

$\displaystyle \small 2\tfrac{1}{4} \cdot n = 4\tfrac{1}{2} \cdot 4\tfrac{2}{3}$

Rewrite with improper fractions and solve:

$\displaystyle \small \small \frac{9}{4} \cdot n = \frac{9}{2} \cdot \frac{14}{3} = \frac{3}{1} \cdot \frac{7}{1} = \frac{21}{1}$

$\displaystyle \small n= \frac{21}{1} \div \frac{9}{4} = \frac{21}{1} \cdot \frac{4}{9} = \frac{7}{1} \cdot \frac{4}{3} = \frac{28}{3} = 9 \frac{1}{3}$

So the correct choice is $\displaystyle \small 9 \frac{1}{3}$.

$\displaystyle \textup{Set up an equation with the two proportions: }\frac{3}{5}=\frac{x}{100}$

$\displaystyle \textup{Cross multiply and solve: }5x=300\;\;\;\;\;\;\;\;\;x=60$

Set up a proportion, with miles driven on top and the time (in minutes) on the bottom:

$\displaystyle \frac{10}{24} = \frac{25}{x}$

Then, cross multiply:

$\displaystyle 10x = 24(25)$, or

$\displaystyle 10x = 600$

Finally, dividing both sides by 10 gives:

$\displaystyle x = 60$ minutes.

To solve the equation, you can set up a proportion with $\displaystyle x$ as the cups of sugar needed for making $\displaystyle y$ cookies. In this case, we know that it takes 6 cups of sugar to make 24 cookies, so we can set up the proportion as $\displaystyle \frac{x}{y}=\frac{6}{24}$. Since we know that we need to make 16 cookies, we can substitute 16 for $\displaystyle y$, $\displaystyle \frac{x}{16}=\frac{6}{24}$. Cross multiply the fractions to get $\displaystyle 24x=96$. Now, solve for $\displaystyle x$ to get a solution of 4.

$\displaystyle \textup{Probability}= \frac{\textup{desired outcomes}}{\textup{total outcomes}}$

$\displaystyle \textup{ First find out how many red and white marbles there are.}$

$\displaystyle \textup{Red: }\frac{2}{5}=\frac{r}{60}\;\;\;5r=120\;\;\;r=24\;\;\;$

$\displaystyle \textup{White: }\frac{1}{4}=\frac{w}{60}\;\;\;4w=60\;\;\;w=15$

$\displaystyle \textup{Blue: }b = 60-24-15\;\;\;\;\;b=21$

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

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

where $\displaystyle x$ is the ounces of chocolate chips needed to make 900 cookies.

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

Proportions are useful for solving many types of problems, but here our equation itself is a proportion.

To solve, we cross-multiply: the numerator of one side times the denominator of the other and vice versa. We are left with

 $\displaystyle x^{2}+4x=60$ or

 $\displaystyle x^{2}+4x-60=0$

A simple FOIL gives us $\displaystyle (x-6)(x+10)=0$

so our solutions are $\displaystyle x=6$ and $\displaystyle x=-10$.

To solve this equation, we need to set up a simple proportion. Since the variables $\displaystyle x$ and $\displaystyle y$ are already in use, let's call the quantity that we are solving for $\displaystyle z$. From the given information, we know we can use the proportion $\displaystyle \frac{9x}{17y} = \frac{24x}{z}$. Cross-multiplication yields $\displaystyle (9x)(z) = (24x)(17y)$. Dividing by the common term of $\displaystyle x$ and simplifying the right side gives us $\displaystyle 9z = 408y$, so our solution must be $\displaystyle 45.3y$.