Math Word Problems: Solving Number Problems Part 4

This is the fourth and last part of the Number Word Problem Solving Series, the first subtopic in the Word Problem Solving Series.   In this post, I will post more word problems with solutions. We start with the tenth problem in the series.

PROBLEM 10

There are three consecutive numbers. The sum of the first two is 20 more than the third. What are the numbers?

Solution

Let x be the first number, x + 1 be the second number, and x + 2 be  third number.  As the problem says, the sum of the first two, x +(x + 1) is 20 more than the third. This means that if we add 20 to the third number, (x + 2) + 20, it will be equal to the sum of the sum of the first two. We now set up the equation

x + (x + 1) = (x + 2) + 20.

Simplifying, we have 2x + 1 = x + 22. This means that x = 21. So, the three consecutive numbers are 21, 22, and 23.

Checking the Answer

The sum of the first two integers 21 + 22 = 43. This is 20 more than 23, the third number. So, we are correct.

PROBLEM 11

In a three digit number, the tens digit is half the hundreds digit. The ones digit is 1 less than the tens digit. If the sum of the digits is 15, what is the number.

Solution

Let x be hundreds digit. The tens digit is half of it, so it’s \frac{1}{2}x. Then, the ones digit is 1 less than the tens digit or \frac{1}{2}x - 1. Since the sum of the three digits is 15, we can set up the equation

x + \frac{1}{2}x + (\frac{1}{2}x - 1) = 15.

Multiplying both sides by 2, we have

2x + x + (x - 2) = 30.

That gives us 4x - 2 = 30, 4x = 32 and x = 8. Therefore, the tens digit is \frac{1}{2}(8) = 4 and the ones digits is 4-1 = 3. So, the number is 843.

Checking the Answer

The tens digit 4 is half of the hundreds digit 8. The ones digit is 3, one less than the tens digit.

PROBLEM 12

The sum of two numbers is 61. Three times the smaller is 13 less than the larger.

Solution

Let x be the smaller number and 61-x be the larger number. Three times the smaller,  3x is 13 less than the larger. This means that if we add 13 to 3x, it will be equal to the larger number which is 61 - x. So, we set up the equation

3x + 13 = 61 - x

Simplifying, we have 4x = 48 which means that x = 12. The other number is 61-12=49.

Checking the Answer

Left as an exercise.

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In the next series, we will discuss word problems involving age. We will have 12 sample problems with solutions.

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