P.8 Modeling with Equations
Writing and Solving Functions
Word Problems
1. Read the problem carefully several times and decide what number or numbers are asked for.
2. Choose a variable to represent one of the numbers asked for or described in the problem. A
sketch or a chart may be helpful.
3. Write an open sentence representing the relationship(s) stated or implied in the problem.
4. Solve the open sentence.
5. Check your results with the requirements stated in the problem.
Pythagorean Theorem—ONLY WORKS FOR RIGHT TRIANGLES
𝑎2 + 𝑏 2 = 𝑐 2 where c is the hypotenuse, the side opposite the right angle
Useful Formulas to remember
Examples
1. The length of a rectangle is 3 times the width. If the length is increased by 4cm. and the width is
decreased by 1cm. the perimeter will be 102cm. Find the dimensions of the original rectangle.
2. A triangular sail has a perimeter of 57ft. Side a is 3ft shorter than twice side b, and side c is 4ft
longer than side b. Find the length of each side.
3. A pair of shoes cost $29.95. They are on sale for 20% off. How much will a customer pay if
there is an 8% tax on the shoes?
4. A rectangular park is three blocks longer than it is wide. The area of the park is 40 square
blocks. If w represents the width, write an equation in terms of w for the area of the park. Find
the length and the width of the park.
5. The length of a rectangular garden is twice its width. The garden is surrounded by a rectangular
concrete walk having a uniform width of 4 feet. If the area of the garden and the walk is 330
square feet, what are the dimensions of the garden?