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For Applied Math courses for Information Technology students, Business Math and Pre-Programming courses. Centered on problem solving, this text is designed to build the skills that are essential for a career in information technology. The text provides a carefully selected set of mathematical tools and begins with an easy-to-use problem solving methodology. Online math solver with free step by step solutions to algebra, calculus, and other math problems. Get help on the web or with our math app.
The following are some examples of problem solving strategies.
Explore it//Act it/Try it (EAT) method (Intermediate)
Explore It/Act It/Try It (EAT) Method (Intermediate)
In this lesson, we will look at some intermediate examples of the Explore it//Act it/Try it (EAT) method of problem solving strategy.
Example:
Allen has to ferry a cat, a chicken and a sack of grain across a river. His small boat is big enough to carry himself and only one of the three items at any one time. He must not leave the cat and the chicken alone or else the cat will attack the chicken. He also must not leave the chicken and the sack of grain alone or else the chicken will eat the grain. Find the least number of trips Allen needs to safely transport all the items to the other side of the river.
Solution:
Example:
Marcus bought two antique lamps for $50 each. Later he sold one for $60, but he changed his mind and bought it back for $70. Then he sold it again for $80. But since there was no one interested in the first lamp, he offered it for 10% less than its original cost, and finally managed to sell it. Did he make or lose money, and how much?
Solution:
All the ‘buy’ transactions: 2 × 50 + 70 = $170
All the ‘sell’ transactions: 60 + 80 + 45 = $185
Marcus made $15
Example:
Without moving 6 adjacent numbers on the face of a clock, rearrange the other six so that the sum of every pair of adjacent numbers is a prime number.
Solution:
11, 12, 1, 2, 3, 4 (not moved) followed by 9, 10, 7, 6, 5, 8
Example:
Julia bought a T-shirt that costs RM28 and paid for it exactly using 7 pieces of notes. What were the 7 pieces of notes that she used?
Solution:
10, 5, 5, 5, 1, 1, 1
10, 10, 2, 2, 2, 1, 1
5, 5, 5, 5, 5, 2, 1
Example:
Four stamps are to be torn from the sheet shown below. The four stamps must be intact so that each stamp is joined to another stamp along at least one edge. Find the possible patterns for these four stamps.
Example:
Yellow, white, green and red counters are arranged in a row. The red counter is to the left of the green counter and to the right of the yellow counter. The white counter is to the left of the green counter and not next to the yellow one. What are the colours of the counters in the row from left to right?
Solution:
Given: The red counter is to the left of the green counter and to the right of the yellow counter.
- Yellow counter is to the left of red counter
- Red counter is to the left of the green counter
Given: The white counter is to the left of the green counter and not next to the yellow one
- White counter is to the left of the green counter
- White counter is not next to the yellow counter
- White counter is between red counter and green counter.
So the order is: Yellow, Red, White and Green.
Example:
The figure below is arranged using 16 matchsticks to form 5 squares. Rearrange exactly 2 of the matchsticks to form 4 squares of the same size, without leaving any stray matchsticks.
Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
Related Pages
Solving Word Problems Using Block Models
Heuristic Approach to Problem-Solving
Algebra Lessons
Problem Solving Strategies
The strategies used in solving word problems:
- What do you know?
- What do you need to know?
- Draw a diagram/picture
Solution Strategies
Label Variables
Verbal Model or Logical Reasoning
Algebraic Model - Translate Verbal Model to Algebraic Model
Solve and Check.
Solving Word Problems
Step 1: Identify (What is being asked?)
Step 2: Strategize
Step 3: Write the equation(s)
Step 4: Answer the question
Step 5: Check
- Show Video Lesson
Problem Solving Strategy: Guess And Check
Using the guess and check problem solving strategy to help solve math word problems.
Example:
Jamie spent $40 for an outfit. She paid for the items using $10, $5 and $1 bills. If she gave the clerk 10 bills in all, how many of each bill did she use?
Problem Solving : Make A Table And Look For A Pattern
- Identify - What is the question?
- Plan - What strategy will I use to solve the problem?
- Solve - Carry out your plan.
- Verify - Does my answer make sense?
Example:
Marcus ran a lemonade stand for 5 days. On the first day, he made $5. Every day after that he made $2 more than the previous day. How much money did Marcus made in all after 5 days?
What Is Math Problem Solving
- Show Video Lesson
Find A Pattern Model (Intermediate)
In this lesson, we will look at some intermediate examples of Find a Pattern method of problem-solving strategy.
Example:
The figure shows a series of rectangles where each rectangle is bounded by 10 dots.
a) How many dots are required for 7 rectangles?
b) If the figure has 73 dots, how many rectangles would there be?
Solution:
| Rectangles | Pattern | Total dots |
| 1 | 10 | 10 |
| 2 | 10 + 7 | 17 |
| 3 | 10 + 14 | 24 |
| 4 | 10 + 21 | 31 |
| 5 | 10 + 28 | 38 |
| 6 | 10 + 35 | 45 |
| 7 | 10 + 42 | 52 |
| 8 | 10 + 49 | 59 |
| 9 | 10 + 56 | 66 |
| 10 | 10 + 63 | 73 |
Solving Math Equations
a) The number of dots required for 7 rectangles is 52.
b) If the figure has 73 dots, there would be 10 rectangles.
Example:
Each triangle in the figure below has 3 dots. Study the pattern and find the number of dots for 7 layers of triangles.
Solution:
| Layers | Pattern | Total dots |
| 1 | 3 | 3 |
| 2 | 3 + 3 | 6 |
| 3 | 3 + 3 + 4 | 10 |
| 4 | 3 + 3 + 4 + 5 | 15 |
| 5 | 3 + 3 + 4 + 5 + 6 | 21 |
| 6 | 3 + 3 + 4 + 5 + 6 + 7 | 28 |
| 7 | 3 + 3 + 4 + 5 + 6 + 7 + 8 | 36 |
The number of dots for 7 layers of triangles is 36.
Example:
The table below shows numbers placed into groups I, II, III, IV, V and VI. In which groups would the following numbers belong?
a) 25
b) 46
c) 269
| I | 1 | 7 | 13 | 19 | 25 |
| II | 2 | 8 | 14 | 20 | 26 |
| III | 3 | 9 | 15 | 21 | 27 |
| IV | 4 | 10 | 16 | 22 | |
| V | 5 | 11 | 17 | 23 | |
| VI | 6 | 12 | 18 | 24 |
Solution:
The pattern is: The remainder when the number is divided by 6 determines the group.
a) 25 ÷ 6 = 4 remainder 1 (Group I)
b) 46 ÷ 6 = 7 remainder 4 (Group IV)
c) 269 ÷ 6 = 44 remainder 5 (Group V)
Example:
The following figures were formed using matchsticks.
a) Based on the above series of figures, complete the table below.
| Number of squares | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Number of triangles | 4 | 6 | 8 | 10 | ||||
| Number of matchsticks | 12 | 19 | 26 | 33 |
b) How many triangles are there if the figure in the series has 9 squares?
c) How many matchsticks would be used in the figure in the series with 11 squares?
Solution:
a)
| Number of squares | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Number of triangles | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 |
| Number of matchsticks | 12 | 19 | 26 | 33 | 40 | 47 | 54 | 61 |
Help Solving Math Word Problems
b) The pattern is +2 for each additional square.
18 + 2 = 20
If the figure in the series has 9 squares, there would be 20 triangles.
c) The pattern is + 7 for each additional square
61 + (3 x 7) = 82
If the figure in the series has 11 squares, there would be 82 matchsticks.
Example:
Seven ex-schoolmates had a gathering. Each one of them shook hands with all others once. How many handshakes were there?
Solution:
| A | B | C | D | E | F | G |
| A | ||||||
| B | ● | |||||
| C | ● | ● | ||||
| D | ● | ● | ● | |||
| E | ● | ● | ● | ● | ||
| F | ● | ● | ● | ● | ● | |
| G | ● | ● | ● | ● | ● | ● |
| HS | 6 | 5 | 4 | 3 | 2 | 1 |
Total = 6 + 5 + 4 + 3 + 2 + 1 = 21 handshakes.
The following video shows more examples of using problem solving strategies and models.
Question 1: Approximate your average speed given some information
Question 2: The table shows the number of seats in each of the first four rows in an auditorium. The remaining ten rows follow the same pattern. Find the number of seats in the last row.
Question 3: You are hanging three pictures in the wall of your home that is 16 feet wide. The width of your pictures are 2, 3 and 4 feet. You want space between your pictures to be the same and the space to the left and right to be 6 inches more than between the pictures. How would you place the pictures?
The following are some other examples of problem solving strategies.
- Explore it/Act it/Try it (EAT)
Explore it/Act it/Try it (EAT) Method (Basic)
Explore it/Act it/Try it (EAT) Method (Intermediate)
Explore it/Act it/Try it (EAT) Method (Advanced) - Finding A Pattern
Finding A Pattern (Basic)
Finding A Pattern (Intermediate)
Finding A Pattern (Advanced)
Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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