The ratio of $y$ to $x$ equal 3 means $\displaystyle \frac{y}{x}=3$ or $y=3x$. Translating "the sum of $y$ and $x$ is 80" into an equation yields $y+x=80$. Substituting $y=3x$ this into the second equation yields $3x + x = 80$ or $4x = 80$ therefore $x = 20$ and $y=60$

Correct Answer is C. Let the number of chickens, pigs and horses on Richard's farm be $c, p$, and $h$. Then forming the given ratio yields $c : p : h = 33 : 17 : 21$ or $\displaystyle \frac{c}{33}=\frac{p}{17}=\frac{h}{21}=k$ where $k$ is a positive integer. Then $c=33k, p=17k$, and $h=21k$.

Then the total number of pigs and horses is $17k + 21k = 38k$; and the total number of pigs, horses and chickens is $17k + 21k + 33k = 71k$.

Hence, the required fraction equals $38k/71k = 38/71$.

First he lays $x$ bricks for $y$ hours which is $x\cdot y=xy$. Then he does $x/2 \cdot 2y=xy$ so in total the lays $xy+xy=2xy$

As the distance on the map increases so does the actual distance. Hence, we set up a direct proportion. Let $x$ be the actual distance between the cities. Forming the proportion yields $\displaystyle \frac{1 \text{in}}{150 \text{mi}}=\frac{3\frac{1}{2}\text{ in}}{x \text{ mi}}$. Solving for $x$ we get $x=525$

Since 1 minute = 60 seconds and 1 hour = 60 minutes, it follows that 1 hour = (60)(60), or 3,600 seconds. Using this conversion factor, the space station's average speed of 4.76 miles per second is equal to an average speed of $$\frac{4.76 \text {miles}}{\text{second}} \times \frac{3600\text{ seconds}}{\text{hour}}=\frac{17136\text{ miles}}{\text{hour}}$$ or 17,136 miles per hour.

Correct Answer is D. The total number of students in the class is 15 + 25 = 40. Now, translate the main part of the sentence into a mathematical equation: $\displaystyle x\% \cdot 40=15$. This is equivalent to $\displaystyle \frac{x}{100}\cdot 40=15$ or $\displaystyle \frac{40}{100} \cdot x=15$. Simplify by 20 we get $\displaystyle \frac{2}{5} \cdot x=15$. Solving for $x$ we yield $2x=75$ or $x=37.5$

Correct Answer is C. The population increased from 12000 to 15000. Hence, the change in population was 3000. Now, translate the main part of the sentence into a mathematical equation: $$\text{Percent of Change:}= \displaystyle \frac{\text{Amount of Change}}{\text{Original Amount}}\times 100\%$$ $$\displaystyle \frac{3000}{12000}\times 100\%=\frac{1}{4} \times 100\%=25\%$$

If $r$ is the original radius then the new radius is $(1+0.25)r=1.25r$. New area of the circle will be: $A_{new}=\pi(1.25r)^2=(1.25)^2(\pi r^2)=1.5625(\pi r^2)=(1+0.5625)A_{old}$ Thus, we can see that area increased by 56.25\%

The probability of an event $A$, written $P(A)$, is the ratio of the number of favorable outcomes of an experiment to the total number of possible outcomes of the experiment. $$\displaystyle P(A)=\frac{\text{number of Favorable outcomes}}{\text{number of Possible outcomes}}$$ $\displaystyle P=\frac{\text{number of Favorable outcomes}}{\text{number of Possible outcomes}}=\frac{\text{Animals or Surfing}}{\text{All Students Who Remembered Dreams}}=\frac{x+3}{10+3+2+x+8}=\frac{x+3}{23+x}$
It is given that $\displaystyle \frac{x+3}{23+x}=\frac{1}{5}$ and by solving for $x$ we get $x=2$