The following steps are recommended in solving word problems in mathematics: READ, KNOW, PLAN, SOLVE, and CHECK. There may be many ways to solve a problem, but for our purpose, we will adhere to these steps as much as we can. If we do this, solving word problems becomes easier. Later, when you have mastered these steps, you may develop your own more effective way of solving a problem.
Problem 1
The length of a rectangle is 3 times greater than its width. Write an expression to represent its perimeter.
If you represent x = width, how will you represent the length? 3x, since the length is 3 times greater than the width.
What formula should you use to answer this problem? Yes, the perimeter of the rectangle P= 2L +2w, where L is the length and W is the width.
P= 2L + 2W
= 2(3x) + 2(x)
= 6x + 2x
= 8x units
Problem 2
The sum of two numbers is 119. The second number is eight more than twice the first number. What are the numbers?
To solve the problem, we follow these steps:
a. Read. Analyze the problem carefully and get a general idea of what is required.
b. Know. Determine what is asked and what are given in the problem.
The problem asked for two numbers. The sum of the two numbers is 112.
The second number is eight more than twice the first.
c. Plan. Make representation of the unknown.
Let x = the first number
2x + 8 = the second number
d. Solve. Set up the equation and solve for the unknown.
x + 2x + 8 = 119
Solution: x + 2x + 8 = 119
3x + 8 – 8 = 119 – 8 (APE)
3x = 111
1 (3x) = (111) (MPE)
3
x = 37 → the first number
2x + 8 = 2(37) + 8 = 82 → the second number
Check. We only check whether the sum of the two numbers is 119.
37 + 82 119
119 = 119 which is true!
Therefore, the required numbers are 37 and 82
Problem 3
The length of a rectangle is one less than three times its width. If the perimeter of the rectangle is 46 units, find the length and width of the rectangle.
We solve the problem, by following the following steps.
a. Read. Analyze the problem carefully and get a general idea of what is required.
b. Know. Determine what is asked and what are given in the problem.
The perimeter of the rectangle is 46.
The length is one less than three times its width.
c. Plan. Make a representation of the unknown.
let w = width
3w– 1 = length
d. Solve. Set up the equation and solve for the unknown.
We recall that the formula for the perimeter of a rectangle is P = 2l + 2w where l
is the length and w is the width. By substitution, we have the following equation:
2(3w – 1) + 2w =46
Solution: 2(3w – 1) + 2w = 46
6w – 2 + 2w = 46 Distributive Property
8w – 2 + 2 = 46 + 2 APE
1 · 8w = 1 · 48 MPE
8 8
w = 48
8
w = 6 → the width
3w – 1 = 3(6) – 1 = 17 → the length
e. Check. We verify whether the perimeter of the rectangle is 46.
46 = 2(6) + 2(17)
46 = 12 + 34
46 = 46