Algebra & word problems tutorial Algebra is a common question topic in the GRE and if you include word problems which are really just algebra problems in disguise then even more of GRE quantitative questions are algebra problems. For many of these word problems the most difficult part of the question is understanding exactly what they are telling you and what you need to find out.This tutorial will assume that you have already worked through our 'Fractions' and 'Exponents, ratios and percents' tutorials. It will also assume that you a fair knowledge of algebra. For example you should be able to solve the following equation to find a.2a + 3= 11a= ?solution at the bottom of this pageSolve this problem by finding the value for a. This tutorial will begin by giving you two methods for making sense of and solving word problems. Then we will revise the solution of quadratic equations and finally look at substitution techniques which will help when you do not know how to find the solution to a question. Solution: a = 4 Word problems with equationsWe will begin with an example of a word problem and then look at how to use equations to solve it .Carl has twice as much money invested in stocks as in bonds. Stocks earn 10% interest per year and bonds 5% per year. If Carl earned a total of $800 dollars from his stocks and bonds last year how much money did he have invested in stocks?A$9,600B$8,000C$6,400D$4,000E$3,200If you feel brave you can have a go at it now. My advice would be to follow these guidelines.Summarize: Write equations, which contain the information given to you in the question. Use sensible variable names for example the first letter of the thing that the variable represents. Identify answer i.e. write down exactly what you are looking for.Solve: find the solution for the equstions you have written down. If you have had a go at the question then check your answer. If not then we will answer the question together. Summarize using equationsIn the question you are given a great deal of information and you need to be able to summarize it in a more manageable form. Often it is a good idea to translate the question into equations. It is important to use variable names that will make sense to you when you are translating these questions into equations.'Carl has twice as much money invested in stocks as in bonds. Stocks earn 10% interest per year and bonds 5% per year. If Carl earned a total of $800 dollars from his stocks and bonds last year how much money did he have invested in stocks?' We will use 'S' to represent stocks and 'B' to represent bonds. Using the first letters of each word makes it easy to remember which is which and avoids any confusion that might arise from using more traditional variable names such as 'x' and 'y'.'Carl has twice as much money invested in stocks as in bonds.'Translates to:S = 2B Note: many people get confused with the phrase 'twice as much' and write 2S = B. This is a very common mistake and must be avoided. If you find that you get confused writing the equation try replacing the variables with numbers and then read the sentence again to see if it makes sense. For example in this case if S = 2B, then if B = 1, S = 2. This makes sense because stocks are '2' which is twice as much as bonds which are '1'.'Stocks earn 10% interest per year and bonds 5% per year. If Carl earned a total of $800 dollars from his stocks and bonds last year...'Stocks earned 10% of S and bonds earned 5% of B and this totaled $800 so,( 10% S ) + ( 5% B ) = 800It is also important to write down what you are trying to find. It is all to easy to do the correct working and get to a related or intermediate answer which you find in the list of answers A-E and to choose it in your haste to finish the question.'...how much money did he have invested in stocks?'You are trying to find the amount in stocks so write downS = ? To summarize we have:S= 2B( 10% S ) + ( 5% B )= 800S= ?Two equations with two unknowns so we can solve them. Solving equationsWe have already done much of the work in solving this problem by changing it from the word problem 'Carl has twice as much money invested in stocks as in bonds. Stocks earn 10% interest per year and bonds 5% per year. If Carl earned a total of $800 dollars from his stocks and bonds last year how much money did he have invested in stocks?' to the algebraic problem S= 2B( 10% S ) + ( 5% B )= 800