Table of Contents
Solving Word problems
Solving problems related to addition and subtraction is made easier by observing aspects of a problem. For this, you need to consider the following questions.
- What is given?
First, we need to identify the data that has been provided.
- What to find out?
Then, we need to figure out what we need to calculate.
- How do we find out?
Finally, we need to analyze which method of operation has to be carried out with the given values so that we can arrive at the required answer.
For example:
Example 1:
Liam has 1000 books in his library. If he bought 500 more and gave away 300 books, how many books does he have in his library now?
Solution:
Understand the problem
What is given?
- Liam has 1000 books.
- He bought 500 more.
- He gave away 300 books.
What to find out?
- How many books does Liam have now?
How will you solve it?
- Add 1000 and 500 to find out how many books Liam has.
- Then subtract 300 from the sum to find out how many books Liam has now.
Step 1:
Let k be the initial number of books.
k = 1000 + 500
Step 2: Let n be the unknown difference after Liam gave away 300 books.
\( n-k=300 \)
\(\Rightarrow n~=~1500-300 \)
\(\therefore n~=~1200 \)
So, Liam has a total of 1200 books in his library.
Solved Examples
Example 1:
Harry has 10 pencils. He bought 5 more pencils.
If he has used 2 pencils, how many pencils are left with him?
Solution:
Initially, Liam had 10 pencils, and later he bought 5 more.
Liam has 10 + 5 = 15 pencils.
Since Liam has used 2 pencils.
The number of pencils he still has is,
= 15 – 2
= 13
Example 2:
Leah and Jay decide to play a game. They need to fill a huge container each with as many items as possible so that one container weighs more than the other. The container that weighs the most wins. It is known that Leah’s container weighs 542 pounds, and both containers weigh 1276 pounds together. By what difference does the winner win?
Solution:
Let the weight of Jay’s container be x pounds.
Since both containers weigh 1276 pounds, the weight of Jay’s container can be given as,
\(x=1276-542\)
\(x~=~734 \)
734 > 542.
734 – 542
Hence, Jay wins the contest by 192 pounds.
Example 3:
A construction company uses 200 fewer rods in constructing building A than building B. There were 624 rods used in building B and 721 rods were used in constructing C. How many rods does the company use to construct building A? Also, find the total number of rods that were used for all three buildings.
Buildings | Rods used |
|---|---|
A | ? |
B | 624 |
C | 721 |
Solution:
Step 1: How many rods are used in building A?
Let \(x\) be the number of rods used in building A
Then,
\(x~=~624-200\)
\(x~=~424\)
Step 2: Find the total number of rods used in all three buildings.
Let \(y\) be the total number of rods used in the three buildings.
Then,
\(y~=~x+624+721\)
\(y~=~424+624+721\)
\(\therefore y~=~1769\)
So, the total number of rods used in all three buildings is 1769.
As the name suggests, two-step addition or subtraction involves two steps. In each step, one equation is solved. After the second step, we arrive at the final answer.
Let us understand this with the help of an example. Say you have 10 balloons, to which you add 3 more. Now you have 10 + 3, which is 13 balloons. If you burst 3 of them, you will be left with 13 – 3 = 10 balloons, which is the number of balloons we started off with. Hence, the addition and subtraction of the same numbers keeps the initial number the same.