Algebra and its applications are quite vast, the boundaries of algebra are not confined to the simple problems of addition, subtraction, multiplication or division. In fact, algebra has spread its wings in almost all sections irrespective of the field, such as engineering, medical, commerce, Geology, etc. Since, it is one of the most extensive topics in the GRE syllabus, therefore it has also become one of the most disliked topics for majority students. Let’s discuss this topic in detail and you can rest assured because algebraic applications is no monster neither it is an Everest that you can’t achieve.

The most important step of solving any word problem is to translate the verbal descriptions into an algebraic expression. Let us understand it through some examples:

- The cubes of x multiplied by 9, and then add the product to 25. It can be represented as 9x
^{3}+ 25 - If Priya’s income is p and is increased by 25% then her new pay will be 1.25p.
- Suppose there is a container containing z gallons of liquid chocolate and you have to divide it among 7 people. The distribution should be made in such a way that 2 particular person gets exactly 1 gallon of chocolate and rest amount is to be distributed equally among the rest people. Express it in mathematical notation:

In mathematical form it can be represented as: \(\small \frac{z – 2}{5}\) .

Importance of expressing verbal descriptions into algebraic expression:

- It make questions easier to solve
- It reduces many irrelevant information
- Only mathematical notation is left, so no need of bugging your head with grammar and complex English words.

Let’s solve a problem and understand the algebraic expressions in further details.

**Question**: A maximum score of 550 can be scored in subject of Psychology. There are 5 homework sets carrying 50 points, through which this score can be obtained along with three exams associated with the homework set carrying 100 points each. Dany received a score of 45, 25, 34, 48, and 31 and his score in first two exams are 87 and 76. Assume that grades are assigned using a standard scale and no weights are assigned to any of the grades, and then is it possible for Dany to receive an A in the Psychology? If yes, then what should be his minimum score in the third test? What should be his score to get a B?

**Solution**: Let us assume that the minimum score to be achieved by Dany in third test is ‘x’.

According to the question there are no weights on the grades. So, the grades will be computed according to the percentage.

Hence, it becomes: \(\small \frac{Actual \; Score}{Maximum \; Possible \; Score} = Percentage \; of \; Grade\)

Since, standard scale is being used, so if Dany’s percentage score is equal to or higher than 0.9 then only he can get an A. Similarly, percentage score in the range of 0.8 and 0.9 will give him grade B.

It given that total score is 550 and Dany’s scores are:

45 + 25 + 34 + 48 + 31 + 87 + 76 + x = 346 + x

According to the formula specified above

\(\small \frac{Actual \; Score}{Maximum \; Possible \; Score} = Percentage \; of \; Grade\).- \(\frac{346+x}{550}=0.9\)
- 346 + x = 0.9 × 550
- 346 + x = 495
- x = 495 – 346
- x = 149

Now, this is a problem as the exam is on 100 marks. So, it is impossible for Dany to get an A in Psychology. But he can get a B if he scores

- \(\frac{346+x}{550}=0.8\)
- 346+x= 440
- x=440-346
- x = 94.

Dany needs a minimum score of 94 to get grade B in Psychology.

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