Question 640285
We know that a van goes 150 miles per 6 gallons.  In other words:

{{{150 miles/6 gallons of gas}}}

So, our proportion will look like this:

{{{150 miles/6 gallons of gas = 500 miles/x gallons of gas}}}

Let's take out the words from our equation:

{{{150/6 = 500/x}}}

When working with proportions (fractions) involving a variable, in this case x, we  can multiply the numerator on the left side by the denominator on the right, and multiply the denominator on the left side by the numerator on the right:

{{{150*x = 6*500}}}, which gives us
{{{150x = 3000}}}

We need to get x by itself on the left side of our equation, so we need to do the opposite of what's being done to x on the left side.  X is being multiplied by 150, so to get x by itself, we need to divide both sides by 150, since division is the opposite of multiplication:

{{{(150x)/150 = 3000/150}}}, which equals

{{{x = 20}}}

Therefore, 500 miles will use 20 gallons of gas