We have  known values and  unknown value. We have a total and that these  colors add up to .

Let's represent the colors with variables corresponding to the first letter of the color. .

Now, plug in the values that are known. Final answer is . 

To simplify we add the constants which results in:

Take every word and translate into math. What a difference means, is that  is the first number subtracting .

The  part is  times something means that you need to multiply  to something which is .

The  part is quotient. 

Anytime you take a quotient of  and ,  is the in the numerator and  is in the denominator. Therefore the expression is . 

Anytime you see "is" means equal.  

 more than means that you need to add  to something.

That something is  multipled by  or .

Let's just combine them to have an expression of . 

Let's translate into math equations.

First month is  Then for the next month, he adds  to the previous month or  Then, for the next month, he adds another  to the previous month which was  By adding another , this month becomes  For the fourth month, it's just another   added to the previous month which was  The fourth month becomes .

With the total given, lets combine the expressions to get .

Simplifying this we get:

Take every word and translate into math. The sum of something means adding. So that would be . Is means equals something. Putting it all together, we get . 

Take every word and translate into math. Difference means subtracting. So we are subtracting  and . Is means equal something. Putting it all together, we have .

Take every word and translate into math. The product of something means multiplying. So we have . The sum of something means adding. So that would be . Is means equals something. Putting it together, we have . 

Take every word and translate into math. Quotient means dividing, so we have . When it's  and ,  will always be at the numerator of the fraction. Is means equal something. Difference is subtracting and we are subtracting  with  times sum of  and . Times means multiplying and sum means addition. We are multiplying  with . There must be parentheses as the sum of  and  is an expression. Putting it all together, we get . 

Take every word and translate into math. Square root means using a radical sign. So we have . Is means equal something. Next, sum is addition so we have . Since it's squared, we have the whole thing in parentheses raised to the second power like so: . It is tempting to think it's  but if it was, then it should say sum of  and  square. So final answer is . 

Starting with the equation , you want to collect like terms.

Put all of the numbers on one side, and leave only the variable on the other side.

The first step is to subtract  from both sides.

You get .

The next step is to divide both sides by  to get the final answer, .

The trick to answer this question is to identify key words and convert them into mathematical expressions.

Suppose a variable  and  which represents numbers.  If a number is twice the value of the second number, then either:

 or 

The "equal" means , and proceed to the right side of the equation.

Rewrite the mathematical expression for "the sum of both numbers quantity squared".

There are 2 combinations for this question.  Write the equations.

Either of these answers are correct.