Aim 15: How do we solve linear equation word problems?
HW: Handout
Do Now #1: The length of each side of a square is represented by 2x - 1, represent the
perimeter of the square.
Do Now #2: Using only the variable x, represent the sum of four consecutive even
integers.
Word Problems
Identify the variables. Use "Let" statements to identify unknown quantities. The value
being compared is going to be represented by the single variable x.
Let width = x
Let length = 3x + 2
Key terms such as: more than, twice, less than, exceeds, etc. will ultimately help you
write the "Let" statements and the equation.
Solve each equation.
Identify what the question is looking for. " x = " is NOT always the answer.
Check without substitution. Does the answer make sense within the context of the
problem?
Ex. The age of my grandfather is 5 years old. (?!?)
For every linear equation word problem,
1) Find three consecutive integers such that the sum of the first and third is 40.
2) Find three consecutive odd integers whose sum is 255.
3) Find two consecutive even integers such that twice the smaller is 26 less than 3 times
the larger.
HW #14 Answers
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4) Find three consecutive even integers such that the sum of the smallest and twice the second is 20
more than the third.
5) The length of the second side of a triangle is 2 inches less than the length of the first side.
The length of the third side is 12 inches more then the length of the first side. The perimeter
of the triangle is 73 inches. Find the length of each side of the triangle.
6) The length of the base of an isosceles triangle exceeds the length of one of the other sides
by 3 cm. The perimeter of the triangle is 93 cm. Find the length of each of the shorter sides of
the triangle.
7) The perimeter of a rectangular tennis court is 228 ft. If the length of the court exceeds
twice the width by 6 ft, find the dimensions of the court.
8) The length of a rectangle exceeds its width by 4 ft. If the width is doubled and the length is
diminished by 2 ft, a new rectangle is formed whose perimeter is 8 ft more than the perimter of the
original rectangle. Find the dimensions of the original rectangle. (Hint: draw the shapes.)
9) A side of a square is 10 m longer than the side of an equilateral triangle. The perimeter of the
square is 3 times the perimeter of the triangle. Find the length of each side of the triangle.
10) The base of an isosceles triangle and one of its legs have lengths that are consecutive
integers. The leg is longer than the base. The perimeter of the triangle is 20. Find the length of
each side of the triangle.
Sum it up
When representing unknown quantities as expressions we use the variable x for the quantity
being compared. (Most times it is the smallest quantity.)
All other quantities are expressions based off of that x value.
Remember to answer the question. "x = " is not always the answer to the word problem.