Aim #16: How do we solve word problems using linear equations?
HW: Handout
Do Now: 1) The length of each side of a square is represented by 2x - 1, represent
the perimeter of the square.
2) Using only the variable x, represent the sum of four consecutive even integers.
When solving 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.
Example:
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Let width = x, Let length = 3x + 2
Write your algebraic equation.
Solve the equation.
Identify what the question is looking for.
Check by substitution, BUT does the answer make sense within the context of
the problem? Ex. The age of my grandfather is 5 years old. (?!?)
For the following word problems, only a complete algebraic solution will be
accepted.
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
three times the larger.
4) Find three consecutive even integers such that the sum of the smallest and
twice the second is twenty 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 1 foot more than 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 its legs
1
by /4 of a foot. The perimeter of the triangle is 93 in. Find the length of each
side 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 72 inches, 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 24 inches, a new rectangle is formed whose perimeter
is 8 ft more than the perimeter of the original rectangle. Find the dimensions of
the original rectangle. (Hint: draw the two rectangles.)
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 the side of the triangle.
10) The base of an isosceles triangle and its legs have lengths that are
consecutive integers. The legs are longer than the base. The perimeter of the
triangle is 20 m. Find the length of each side of the triangle.
Sum it up
When solving word problems algebraically:
• Represent one of the unknown quantities with a variable and try to relate all the
other unknown quantities (if there are any) to this variable.
• If applicable, sketch a figure illustrating the situation.
• Write an equation that will relate known quantities to the unknown quantities.
• Solve the equation formed in the previous step and write down the answer to
the question. It is important to answer all the questions that you were asked.
Often you will be asked for several quantities in the answer and the equation
will only give one of them.
• Check your answer! Do this by plugging into the equation, but also use intuition
to make sure that the answer makes sense.