How to Solve Number Word Problems Part 2

This is the second part of the the Solving Number  Word Problems Series. In this part, we will discuss how to solve various number problems.  Note that some of these problems are not really number problems per se, but the strategy in solving them is technically the same. You could say that they are really “number problems in disguise.”

We already had three problems in the first part of this series, so let’s solve the fourth problem.

Problem 4

If 8 is subtracted from three times a number, then the result is 34. What is the number?

Scratch work

In the How to Solve Number Word Problems Part 1, I mentioned that sometimes, if it is hard to convert the words in the problem to equations, it is helpful to think of a particular number. For example, in this problem, the phrase is “three subtracted from three times a number.” So, if we choose a number, say for example, 5, we want to subtract 8 from three times 5. In numerical expression, that is 3(5) - 8. So, if a number is x, the expression is 3x - 8. Now, this 3x - 8 results to 42 as stated above. Intuitively, it is saying that 3x - 8 is equal to 42. That’s our equation!

Solution

Let x be the number.

3x - 8 is 8 less than 3 times the number.

Now, 3x - 8 = 34.

3x - 8 + 8 = 34 + 8

3x = 42

x = 14

Check: The problem says that if 8 is subtracted three times the number, the result is 34. Now, three times 14 is 42. Now, if we subtract 8 from 42 the result is 34 and we are correct.

Problem 5

Separate 60 into two parts such that the one exceeds the other by 24. What are the numbers?

Scratch Work

If we separate 60 into two parts, and one part is, for example, 10, then the other part is 60 - 10 which is 50. This means that if one part of 60 is x, then the other part is 60 - x.

Now it says that the larger number exceeds the smaller number by 24. This means that

larger number – smaller number = 24.

The only part left now is to choose which is larger, x or 60 - x. It won’t really matter.

Solution

Let 60 - x be the larger and x be the smaller number.

Then,

(60 - x) - x = 24

60 - 2x = 24.

Subtracting 60 from both sides results to

-2x = -36.

Dividing both sides by -2, we get

x = 18.

So, the smaller number is 18 and the larger number is 60 - 18 = 42.

Check: Is the sum of the two numbers is 60? Does 42 exceed 18 by 24? If both answers are yes, then we are correct.

Problem 6

The sum of the ages of Abby, Bernice, and Cherry is 76. Bernice is twice as old as Abby, while Cherry is 4 years older than Abby. What are the ages of the three ladies?

Scratch Work

As I have mentioned above, some problems are really number problems in disguise. This problem is one of them.

From the problem, it is easy to see that the youngest in the group is Abby. Let us say, Abby is 20. So, Bernice is twice as old or 2(20) = 40 years old. Then, Cherry is four years older than Abby or 20 + 4 = 24.

So, from this analysis, if Abby is x years old, then, Bernice is 2x. Since Cherry is four years older than Abby, then here age is x + 4.

In the first sentence, it says that the sum of the ages of the three ladies is 76. Therefore, we must add their ages (x, 2x and x + 4) and equate it to 76. That is our equation.

Solution

Let x be Abby’s age, 2x be Bernice’s age and x + 4 be Cherry’s age.

x + 2x + (x + 4) = 76

4x + 4 = 76

4x + 4 - 4 = 76 - 4

4x = 72

Dividing both sides by 4, we have x = 18.

So, Abby is 18, Bernice is 2(18) and Cherry is 18 + 4 = 22 years old.

Check: Is the sum of their ages 76?

In the next post in this series, we are going to discuss how to solve problems involving consecutive integers.

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2 Responses

  1. March 19, 2014

    […] introduction to this series, we have learned How to Solve Number Problems Mentally. In Part 1 and Part 2, we have discussed the basic number word problems, and in Part 3, we have learned how to solve word […]

  2. August 20, 2015

    […] (3) How to Solve Number Problems Part 2 […]

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