Math Word Problems: Solving Number Problems Part 2

This is the continuation of the previous post on solving number problems. In this post, I will give three more examples on how to solve word problems about numbers.

PROBLEM 4

One number is smaller than the other by 12. Their sum is 102. What is the smaller number?

Solution

In the previous post, we talked about two numbers, one is being larger than the other. In this problem, the other number is smaller. If a number is 15, and the other number is 6 smaller than it, then that number is 15 - 6. So, in the problem above, if we let n be the number, then n - 12 is the smaller number.  Again, their sum is 102, so we can now set up the equation

Simplifying, we have 2n - 12 = 102. This gives us 2n = 114 which means that n = 57. The smaller number is 57-12 = 45.

Checking the Answer

Is 45 twelve less than 57? Is their sum equal to 102? If the answer to both questions is yes, then we are correct.

PROBLEM 5

Divide 71 into two parts such that one part exceeds the other by 8. What are the two numbers?

Solution 1

Let $let n$ be the smaller and 71 - n be the larger number.  Now, since the larger number exceeds the smaller number by 7, we can form the equation

larger numbersmaller number = 7

which is equivalent to

Simplifying, we have 71 - 2n = 7. This gives us 2n = 78 which implies that the larger number is . The smaller  is .

Solution 2

Same as the solution of Problem 1. I leave this to you as an excercise.

Checking the Answer

Do the two numbers add up to 71. Does the number exceeds the smaller number by 7?

PROBLEM 6

The sum of three consecutive even numbers is 90. What are the three numbers?

Solution

In the previous post, we talked about consecutive numbers. We know that consecutive numbers are numbers in uninterrupted succession. For instance, 10, 11 and 12 are three consecutive numbers.  In effect, if n is the smaller number, the next two numbers are n + 1 and n + 2. However, consecutive even numbers increases by 2 such as 16, 18, and 20. In effect, if n is the smallest number, then n + 2 is the middle number and n + 4  is the largest number. Knowing their sum, we can now set up the equation

Simplifying, we have 3n + 6 = 90. This gives us 3n = 84 and n = 28. So the consecutive even numbers are 28, 30 and 32.

Checking the Answer

Are the three numbers even and consecutive? Is their sum equal to 90? If the answers to both question is yes, then we are correct.

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