Solving Word Questions

Using the part where you need to take the English words and translate them into mathematics is the hardest thing about solving word problems. Usually, you're good after you have the math equation; the actual math involved is always pretty simple. But it can seem almost impossible to work out the exact equation. What follows is a list of tips and suggestions. However, you will need to practice, practice, practice to really understand "how to do" word problems. Let's look at math word problems with answers and solutions here before we proceed further. 

How Can We Solve Them?

Word problem questions have a technique to solve them easily. The technique is to split the solution into 2 parts:

• Convert the English into Algebra.

• Using Algebra to solve the equation we get.

In order to be a good word problem solver, it is important to learn how to turn English into Algebra. How to do it? 

• First, read the entire problem

• If necessary, do a sketch.

• Allocate letters for the values

• Find or figure out Formulas to solve equations  

Let's Discuss How to Convert English into Algebra in Detail: 

The first step to translating and solving word problems effectively is to read the problem entirely with clear understanding. When you've just read half a line, don't start trying to solve it. Try to get a sense of the whole problem first; try to see what data you have first, and then find out what you really need.

Working in a structured way is the second step. Find out everything you need but don't have, then name things. Choose variables to represent the unknowns, specifically marking these variables with what they represent. Draw photographs neatly and mark them. As you go along, explain your logic. And ensure that you know exactly what the issue is really calling for. For two reasons, you need to do this:

• Working clearly helps you to think clearly.

• It will help you translate your final answer back into English to find out what you need.

It can be very disappointing to spend 15 minutes trying to solve a word problem on a test, just to realize that you no longer have a solution for what "x" is for, and you'll have to solve the whole problem over and over again. For that reason, it is important to learn this third step. This step is to search for "key" words. Specific words indicate specific operations of mathematics. Here is a partial list:

• For Addition: increased by, more than, combined, together, a total of, sum, plus, added to, comparatives like greater than. 

• For Subtraction: decreased by, minus, less, the difference between/of, less than, fewer than, left, leftover, after, save, comparatives like smaller than. 

• For Multiplication: of, times, multiplied by, the product of, increased/decreased by a factor of, twice, triple, Each like they got three each. 

• For Division: per, out of, the ratio of, the quotient of, per cent, divide by 100, equal pieces, split, average.

• For Equals: is, are, was, were, will be, gives, yields, sold for, cost. 

• For Geometry formulas: maximize or minimize

• For Distance formulas: Rate, speed

• For Time problems: How long, days, hours, minutes, seconds

NOTE: Do not consider keyword lists as holy content, that is conveyed from above. Use these lists as handy tips instead. But always make use of your head! If you are not sure of the correct translation, use the numbers. If you're not sure about the problem's context, relate it to what you'd encounter "in real life." Most of all, take time to understand how you're doing, and why. When you can explain clearly your work to a fellow student, you're going to be a good math word problem solver.   

Let’s Look at a Few Math Word Problems with Answers

Question: Ram has 20 rupees less than Shyam. How can we write this in an equation?

Ans: Let R = Rupees Sam has

Let S = Rupees Shyam has

Now, if we break the problem since Ram has 20 rupees less than Shyam, we can write it as:

R = S - 20 

Question: Translate "the sum of 5 and x" into an algebraic expression.

Ans: The keyword "sum" tells us that they want us to add the given two quantities. This is translated to:

“5 + x”

The order of the quantity does not matter here, since it is being added. But it's still a great idea to get into the habit of writing things in the specified order because it's going to matter in some contexts. While "x + 5" is technically OK, it's better to use the "5 + x" command, because that's the order they used in English.

Question: Translate "y multiplied by 3" into an algebraic expression.

Ans: The keyword here is very obvious; "multiplied by" means we'll multiply by the given value. The sequence of the terms here is (unknown), and the value is multiplied (the unknown). We put the constant in algebra, however, before the unknown. As order does not matter for multiplication, we can write it as (y)(3) = (3)(y). 

"3y" is the answer. 

Question: Translate "the quotient of y and 5" into an algebraic expression.

Ans: The "quotient" keyword here tells me one of the things is separated into the other. The order of the items here is crucial because of division. Since (the unknown) first comes in the English language, this tells me the fraction is above. Then it means the following: \[\frac{y}{5}\]

Ratio and Proportion Word Problems

Question: The police-lawyers ratio is 5:4 in a party. If the party has a total of 72 members, the number of lawyers in the group are?

Ans: We have a police-lawyers ratio as 5:4

So, Let the number of police be 5x and lawyers be 4x.

So, 5x + 4x = 72 

Therefore, x = 8.

Hence,  the lawyers in the group are 4 x 8 = 32.

Question: For every 6 kg of flour, a certain recipe needs 3 Kg of sugar. How much sugar is required, if 60 Kgs of this sweet are to be prepared?

Ans: Let x Kgs be the required amount of sugar.

It is given, 3Kgs of sugar required for 6Kgs flour which gives us 9Kgs Sweet.

So, In 9 Kgs sweet, 3 kg of sugar is available. For 60 kg of sweet, we have to find the amount of sugar required. And the proportion would be as follows: 

\[\frac{3}{9}\] = \[\frac{x}{60}\]

which gives us x = 20  

Hence, for 60Kgs sweet, 20Kgs sugar is required. 

Fraction Word Problems with Answers

Question: Ram had 120 Apples in his store. He sold 23 of them at 20Rs each. How much did he make by selling those apples?

Ans: First, let us find the number of Apples he sold.

I.e., \[\frac{2}{3}\] x 120 = 80 

So, Ram has sold 80 Apples. 

Now, each Apple costs 20Rs.

Hence, 80 x 20 = 1600

He made 1600 Rs by selling those 80 Apples.  

Worded Percentage Problems

Question: In an annual exam, Mahima secured 332 marks. If she has secured 83 % makes of the total marks, find total marks. 

Ans: Let the total marks be m.

Mahima’s marks = 83% of m

She has secured 332 marks

Hence, 83% of m = 332

⇒  \[\frac{83}{100}\] × m = 332

⇒ m = (332 × 100)/83

⇒ m =33200/83

⇒ m = 400

Therefore, Mahima got 332 marks out of 400 marks.

Conclusion

After you have learned the basic keywords you can solve grade 5 word problems with answers easily. After that translating English word problems into mathematical expressions and equations, different English expressions will be given and you will be told to translate them. You are prepared to dive into hard math word problems with answers, once learn to translate phrases into words and phrases into equations.