Quadratic Word Problems

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Videos, worksheets, solutions, and activities to help Algebra students learn about quadratic word problems.
How to solve word problems using quadratic equations?

Quadratic Equation Word Problems
Solving word problems with quadratic equations - consecutive integer and rectangle dimensions problems.
Examples:
(1) The product of two positive consecutive integers is 5 more than three times the larger. Find the integers.
(2) The width of a rectangle is 5 feet less than its length. Find the dimensions of the rectangle if the area is 84 square feet. How to solve word problem using quadratic equations?
Example: A manufacturer develops a formula to determine the demand for its product depending on the price in dollars. The formula is D = 2,000 + 100P - 6P² where P is the price per unit, and D is the number of units in demand. At what price will the demand drop to 1000 units? Examples:
(1) A rock is thrown skyward from the top of a tall building. The distance, in feet, between the rock and the ground t seconds after the rock is thrown is given by h = -16t² + 4t + 442. How long after the rock is thrown is it 430 feet from the ground?
(2) The product of two consecutive positive integers is 359 more than the next integer. What is the largest of the three integers?
(3) The perimeter of a rectangular concrete slab is 82 feet, and its area is 330 square feet. What is the length of the longer side of the slab? Examples:
(1) Consider a rectangle whose area is 45 square feet. If we know that the length is one less than twice the width, then we would like to find the dimensions of the rectangle.
(a) If we represent the width of the rectangle using the variable W, then write an expression for the length of the rectangle, L, in terms of W.
(b) Set up an equation that could be used to solve for the width, W, based on the area.
(c) Solve the equation to find both dimensions. Why is one of the solutions for W not viable?
(2) A square has one side increased in length by two inches and an adjacent side decreased in length by two inches. If the resulting rectangle has an area of 60 square inched, what was the area of the original square? First, draw some possible squares and rectangles to see if you can solve by guess-and-check. Then solve it algebraically.
(3) There are two rational numbers that have the following property: when the product of seven less than three times the number with one more than the number if found it is equal to two less than ten times the number. Find the rational numbers that fit this description.
(4) Find all sets of consecutive integers such that their product is less than ten times the smaller integer.
(5) Brendon claims that the number five has the property that the product of three less than it with one more is the same as the three times one less than it. Show that Brendon's claim is true and algebraically find the number for which this is true.