Verbal cues include "IS" means equals and "OF" means multiplication.

So the equation to solve becomes

and dividing both sides by gives 

Isolate  in the first equation.

Plug into the second equation to solve for .

Plug into the first equation to solve for .

Now we have both the and values and can express them as a point: .

1st equation:

2nd equation:

Subtract the 2nd equation from the 1st equation to eliminate the "2y" from both equations and get an answer for x:

Plug the value of  into either equation and solve for :

Rewrite  as a compound statement and solve each part separately:

Therefore the solution set is .

The first step in solving this equation is to distribute the 3 and the 4 through the parentheses:

Simplify:

Now, we want to get like terms on the same sides of the equation. That is, all of the terms with an  should be on one side, and those without an  should be on the other. To do this, we first subtract  from both sides:

Simplify:

Now, we subtract 6 from both sides:

This problem is solved using proportions and the following conversion factor:

Let yellow quarts of paint.

Then cross multiply to get .

Multiply both sides by to eliminate the fractions to get .

Then use the distributive property to get .

Now subtract from both sides to get .

Now subtract from both sides to get .

, so we are trying to mail ounces. The total postage becomes .

If the original price of the T-shirt is , increasing the price by 50% means that the new price  is 150% of , or .

If the price is then decreased by 50%, the new price  is 50% of

or

The ratio of  to  is then:

The 's in the numerator and denominator cancel, leaving , or

   .

When multiplying rational expressions, we simply have to multiply the numerators together and the denominators together. (Warning: you only need to find a lowest common denominator when adding or subtracting, but not when multiplying or dividing rational expression.)

In order to simplify this, we will need to factor  and . Because  looks a little simpler, let's start with it first.

We can easily factor out a four from both terms.

.

Next, notice that  fits the form of our difference of squares factoring formula. In general, we can factor  as . In the polynomial  we will let  and . Thus, . 

Now, we can see that.

We then factor . This also fits our difference of squares formula; however, this time  and . In other words, . Applying the formula, we see that

. Now, let's take our factorization one step further and factor , which we already did above.

. 

Be careful here. A common mistake that students make is to try to factor . There is no sum of squares factoring formula. In other words, in general, if we have , we can't factor it any further. (It is considered prime.)

We will then put all of these pieces of information in order to simplify our rational expression.

Lastly, we cancel the factors that appear in both the numerator and the denominator. We can cancel an  and a  term. 

.

The answer is .