## Problem Solving Strategies

This chapter is aimed at solving mathematical problems. In solving these problems, you have to know what you are
trying to solve and find the correct process to go about it. Therefore, you also need to know the basic procedures
and techniques in mathematics.

Problem solving could be summarized using these steps:

1. Read and understand the problem carefully.

2. Identify what the problem asked for.

3. Take note of the data the problem is presenting to you.

4. Determine the possible process you are going to do and use the applicable data in the problem.

Example:

1.     Mr. X has to be at work by 8:00 AM and it would take him 10 minutes to get dressed, 15 minutes to eat, and 40
minutes to ride to his work. What time should he get up to get to his work on time?

Solution:

You should know what time Mr. X would get up in order for him to get to work on time.

What are the data presented in the problem?

10 minutes – to get dressed

15 minutes – to eat

40 minutes – travel time to his work

What process should we use in order to solve the problem?

You need to know the total number of minutes Mr. X takes to prepare before he goes to his work and subtract it
from his target time to be able to know what time he should get up.

10 + 15 + 40 = 65 minutes

Mr. X needs 65 minutes in order for him to prepare and be ready for work. 65 minutes is also equivalent to 1 hour
and 5 minutes.

Now that we know how long he prepares himself, we can now deduct it from the target time which is 8:00 AM.

8:00 AM – 65 minutes = 6:55 AM

Therefore, Mr. X should be awake by 6:55 AM so that he can be at work by 8:00 AM.

#### Try this:

1.    Sammy sells lemonade during summer. On the first week, he sold 32 glasses, on the second he sold 30
glasses and on the last week he sold 35 glasses. How many glasses did he sell for 3 weeks?

Solution:

The problem is asking the total number of glasses of lemonade Sammy sold.

First week – 32 glasses

Second week – 30 glasses

Third week – 35 glasses

32 + 30 + 35 = 97

Therefore, Sammy sold 97 glasses of lemonade in three weeks.

2.    Mr. Rodriguez and his family went on a picnic in the countryside. They had to buy food first so they went to the
nearest grocery along the way which is 5 km from their house. Then they took a 53 km trip to the countryside.
However, they got lost along the way and passed the picnic grounds. They then had to drive back 8km. How far
was the countryside from Mr. Rodriguez's house?

Solution:

The problem wants you to solve how many kilometres is the countryside from the house of Mr. Rodriguez.

From their house to the grocery – 5 km

From the grocery to the countryside – 53 km

The distance they got lost – 8 km

We add up the distance from their house to the grocery and from the grocery to the countryside.
5 km + 53 km = 58 km

However, the problem said that they drove back 8 km because they got lost. So, we subtract the distance they
drove back.
58 km – 8 km = 50 km

Therefore, the distance from the house of Mr. Rodriguez to the countryside is 50 km.

3.    The sign in the grocery says "one free for every 2 purchase of each item". How many would you purchase if
you wanted to get 6 free items?

Solution:

The problem asks how many items you should buy to get 6 free items.

2 items = 1 free

You want to get 6 free items. So,
1 free x 6 pieces = 2 items x 6
6 free items = 12 items

Therefore, in order to get 6 free items, you have to purchase 12 items.