This is a proportion problem. To find \(\displaystyle x\), we can use the cross-multiply method. This methods works by, first, multiplying the numerator of the first fraction with the denominator of the second fraction.  Set this multiplication equal to the multiplication of the denominator of the first fraction with the numerator of the second fraction.  In our problem, this is written as

\(\displaystyle 2(36)=9x\)

\(\displaystyle 72=9x\)

divide by 9

\(\displaystyle \frac{72}{9}=\frac{9x}{9}\)

\(\displaystyle x=8\)

First, translate the problem into a proportion equation. We have the ratio 1:4. Therefore, we have the fraction \(\displaystyle \frac{1}{4}\).  Set that fraction equal to the number of blue (which is 16) marbles divide by the number of red marbles.

\(\displaystyle \frac{1}{4}=\frac{16}{r}\)

We need to find \(\displaystyle r\), the number of red marbles.  Perform the cross multiplication

\(\displaystyle 1r=4(16)\)

\(\displaystyle r=64\)

So there are 64 red marbles.

For this problem, we can divide both sides of the original equation by \(\displaystyle -3\) to obtain our answer. Another way we can solve this problem, however, is by using a proportion, 

\(\displaystyle \frac{3x}{141}=\frac{-x}{y}\)

Cross-multiplication yields the equation 

\(\displaystyle 3xy=-141x\)

Dividing both sides by \(\displaystyle x\) gives us 

\(\displaystyle 3y=-141\)

an equation that can be easily solved to get 

\(\displaystyle y=-47\)

Multiply diagonally so that you get \(\displaystyle 16x+48=28\).

Isolate for \(\displaystyle x\) and you get \(\displaystyle -\frac{20}{16}\).

Simplify and you get \(\displaystyle -\frac{5}{4}\). 

Cross-multiply and you get \(\displaystyle 8x=72x+40.\) 

Isolate for \(\displaystyle x\) and you get \(\displaystyle -\frac{5}{8}\).

\(\displaystyle x\) gallons will allow the car to travel \(\displaystyle y\) miles, or \(\displaystyle 1.6y\) kilometers.

Set up a proportion, where \(\displaystyle d\) is the distance:

\(\displaystyle \small \frac{d}{15} = \frac{1.6y}{x}\)

Solve for \(\displaystyle d\):

\(\displaystyle \small d = \frac{1.6y}{x} \cdot 15\)

\(\displaystyle d = \frac{24y}{x}\)

To solve the proportion, cross multiply.

\(\displaystyle x^2=16\)

\(\displaystyle x=\sqrt{16}\)

\(\displaystyle x=\pm 4\)

The correct answer is \(\displaystyle \pm4\) since both numbers satisfy the original problem.

Cross multiply.

\(\displaystyle \frac{1}{2}=\frac{3}{x}\)

We get 

\(\displaystyle \\1\cdot x=2\cdot 3\\ x=6\).

That's the answer. 

Let's cross multiply.

\(\displaystyle \frac{2}{5}=\frac{x}{3}\)

We have 

\(\displaystyle \\2\cdot 3=5\cdot x \\6=5x\).

Divide both sides by \(\displaystyle 5\). 

\(\displaystyle x=\frac{6}{5}\). 

Let's cross multiply.

\(\displaystyle \frac{3}{4}=\frac{x}{2}\)

We have 

\(\displaystyle \\4\cdot x=3\cdot 2\\4x=6\).

Divide both sides by \(\displaystyle 4\), we get 

\(\displaystyle x=\frac{6}{4}=\frac{3}{2}\).

The answer is reduced and we do that by dividing top and bottom by \(\displaystyle 2\).