Word & Logic Problems

Word problems can utilize a variety of math skills and can be used to apply math formulas and methodologies to practical applications. Ted Ed has an excellent video series on various logic problems involving math, and it can be found here. 

We will explore various examples of different word problems to demonstrate employing different strategies to solve them. 

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Example 1

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Find the area of the rectangle.

W = (2x -3)

L = (3x + 1)

Area is Length x Width. Therefore, this is a polynomial multiplication question.

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Step 1: Multiply binomials

(2x-3)(3x+1) multiply using FOIL

= 6x² + 2x - 9x -3

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Answer = 6x² -7x -3

Here is a video on multiplying binomials for additional information on the topic:

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Example 2

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At a dance recital, there were 220 people. Tickets cost $9 for an adult and $6 for a child. The dance school collected $1614 in ticket sales. How many adults and how many children attended the recital?

This is a two equations, two unknowns problem, or a System of Equations.

Step 1: identify the two unknowns

A = number of adults attending
C = number of children attending

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Step 2: write two equations that represent both unknowns (or variables)

A + C = 220 

we know that there were 220 attendees, and that its composed of the sum of adults and children present

1614 = 9A + 6C 

we know the total collected in sales is the sum of the amount received from adult ticket sales and child ticket sales

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Step 3: solve using substitution

Rearrange the first equation so A = 220 - C

Substitute 220 - C into the A in the second equation

1614 = 9(220-C) + 6C

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Step 4: solve for each variable

1614 = 1980 - 9C + 6C

1614 = 1980 - 3C

-366 = -3C

C = 122

A = 220 - 122
A = 98

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Therefore, there were 122 children and 98 adults at the recital. 

This video shows another similar example:

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Example 3

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Max the dog eats 3 treats on day 1, 5 treats on day 2, 7 treats on day 3, and so on. What is the rate of his treat consumption and on which day will he eat 57 treats?

This is a sequence question.

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Step 1: identify the pattern

Day 1 = 3 treats, Day 2 = 5 treats, Day 3 = 7 treats.

It is going up by 2 treats each day. 

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Step 2: Substitute the values into the general formula to find the day where he will eat 57 treats. 

This time, we know the value of the nth term is 57, but we want to know what n is. 

x_n = a + d(n−1)

57 = 3 + 2(n-1)

57 = 3 + 2n -2

57 = 1 + 2n

56 = 2n

n = 28

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Answer: Day 28

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Teacher Tips

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Ensure that when doing word problems, you identify what the question is looking for and what information is given. 

This can help you decide what type of problem it is and how to solve it. 

If there are more than one unknowns, it is a system of equations. For every unknown (variable) there needs to be an equation. (i.e. x y z would need 3 equations)

This video is a great example of applying logical reasoning:

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