Solving Quadratic Word Problems

This video tutorial by Kirk Wyler from eMath Instruction covers quadratic word problems, focusing on solving real-world scenarios using quadratic equations. The lesson includes exercises on finding rectangle dimensions using area and perimeter, solving integer property problems, and verifying claims with quadratic equations. The tutorial emphasizes the use of factoring and completing the square to solve these equations, providing a comprehensive understanding of quadratic word problems.

What is the expression for the length of a rectangle if the width is represented by w and the length is 10 feet more than twice the width?

• 2w + 10

• w + 10

• w + 20

• 2w + 5

Which equation represents the area of a rectangle with width w and length 2w + 10, given the area is 72 square feet?

• w + 2w + 10 = 72

• w(2w) = 72

• w(2w + 10) = 72

• 2w + 10 = 72

Why is one of the solutions for the width of the rectangle not viable?

• Width cannot be zero

• Width cannot be negative

• Width must be an integer

• Width must be greater than the length

If a rectangle has a perimeter of 48 feet and an area of 135 square feet, which system of equations can be used to find its dimensions?

• w + l = 48 and w * l = 135

• 2w + 2l = 48 and w * l = 135

• w + l = 48 and 2w * 2l = 135

• 2w + 2l = 48 and w + l = 135

What is the length of a rectangle if its width is 9 feet and the length is 24 minus the width?

• 18 feet

• 24 feet

• 9 feet

• 15 feet

Which equation represents the product of one more than three times a number and two less than the number, equaling 43 more than the number?

• (3n + 1)(n - 2) = n + 43

• (3n - 1)(n + 2) = n + 43

• (3n + 1)(n - 2) = 43 - n

• (3n - 1)(n + 2) = 43 - n

What are the two integers that satisfy the equation (3n + 1)(n - 2) = n + 43?

• 4 and -2

• 5 and -3

• 5 and -2

• 6 and -4

Find all sets of two consecutive integers such that their product is eight less than ten times the smaller integer.

• 2 and 3, 7 and 8

• 1 and 2, 8 and 9

• 4 and 5, 5 and 6

• 3 and 4, 6 and 7

What is the other number for which the product of three less than it with one more than it is the same as three times one less than it?

• 1

• 0

• 2

• 3

What is the quadratic equation formed when solving for the number n in the equation (n - 3)(n + 1) = 3(n - 1)?

• n^2 - 5n = 0

• n^2 + 3n = 0

• n^2 + 5n = 0

• n^2 - 3n = 0