Let $\displaystyle 3x, 4x,\text{ and}, 5x$ be the values of the angles.

Since there are $\displaystyle 180$ degrees in a triangle,

$\displaystyle 3x+4x+5x=180$

$\displaystyle 12x=180$

$\displaystyle x=15$

Since we want the value of the smallest angle, find the value of $\displaystyle 3x$.

$\displaystyle 3x=15\times3=45$

First, find the number of red bottles and blue bottles.

Let $\displaystyle x$ be the number of red bottles and $\displaystyle 5x$ be the number of blue bottles. Since there is a total of $\displaystyle 3300$ bottles at the factory,

$\displaystyle x+5x=3300$

$\displaystyle 6x=3300$

$\displaystyle x=550$

There are $\displaystyle 550$ red bottles. Find the value of $\displaystyle 5x$ to find the number of blue bottles.

$\displaystyle 5x=550\times5=2750$

Now, because the question wants to find how many more blue bottles than red bottles there are, subtract the number of red bottles from the number of blue bottles.

$\displaystyle 2750-550=2200$

Let $\displaystyle 2x$ be the number of offensive players and $\displaystyle 5x$ be the number of defensive players.

Since there is a total of $\displaystyle 42$ players on the team,

$\displaystyle 2x+5x=42$

$\displaystyle 7x=42$

$\displaystyle x=6$

We need to find the number of offensive players, so we will need to find the value of $\displaystyle 2x$.

$\displaystyle 2x=6\times2=12$

Out of the 100 tiles, there are nine "A" tiles, twelve "E" tiles, nine "I" tiles, eight "O" tiles, and four "U" tiles.

If the "E" tiles are removed, there will be 

$\displaystyle 9 + 9 + 8 +4 = 30$ vowel tiles.

The number of consonant tiles can most easily be found by adding the number of vowel tiles and blanks:  

$\displaystyle 9 + 12 + 9 + 8 + 4 + 2= 44$.

The rest of the tiles are consonant tiles; subtract from 100 to get

$\displaystyle 100 - 44 = 56$ of them.

Therefore, the ratio of consonant tiles to vowel tiles in the box after removing the "E's" is

$\displaystyle \frac{56}{30} = \frac{56 \div 2 }{30 \div 2 } = \frac{28}{15 }$ - that is, a 28 to 15 ratio.

Let $\displaystyle 2x$ be the amount John takes home and $\displaystyle 3x$ be the amount Michela takes home.

Since their business made $\displaystyle \$36,000$,

$\displaystyle 2x+3x=36000$

$\displaystyle 5x=36000$

$\displaystyle x=7200$

We want to know how much Michela made so we need to find the value of $\displaystyle 3x$.

$\displaystyle 3x=7200\times3=21600$

First, find out how long it takes the factory to produce $\displaystyle 1$ tent.

$\displaystyle \frac{15}{300}=0.05$

Since it takes the factory $\displaystyle 0.05$ minutes to make $\displaystyle 1$ tent, multiply this number by $\displaystyle 9000$ to find how long it takes to make $\displaystyle 9000$ tents.

$\displaystyle 0.05\times9000=450$

It will take the factory $\displaystyle 450$ minutes to make $\displaystyle 9000$ tents.

First, find how many cans of soda Billy can drink in 1 day.

$\displaystyle \frac{12}{4}=3$

Since, he can drink $\displaystyle 3$ cans in $\displaystyle 1$ day, then the following equation will tell us how many cans he drinks in $\displaystyle 2$ days.

$\displaystyle 3\times2=6$

First, find the cost per marker.

$\displaystyle 45\div15=3$

Now, multiply this cost per marker by $\displaystyle 25$, the number of markers we want.

$\displaystyle 25\times3=75$

Set up the following proportion:

$\displaystyle \frac{2}{0.5}=\frac{200}{x}$,

where $\displaystyle x$ is the number of hours it'll take to empty $\displaystyle 200$ gallons.

Now solve for $\displaystyle x$.

$\displaystyle 2x=100$

$\displaystyle x=50$

First, figure out how long it takes Julie to read 1 page.

$\displaystyle 2\div5=0.4$

It takes Julie $\displaystyle 0.4$ minutes to read one page. Now, multiply this by the number of pages she needs to read to find out how long it will take her.

$\displaystyle 0.4\times120=48$

It will take Julie $\displaystyle 48$ minutes to read $\displaystyle 120$ pages.