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 \(\displaystyle 45.3y\).