Download Solving Word Problems on Factoring, Quadratic Equations, and Geometry and more Exams Humanities in PDF only on Docsity!
Chapter 6 _ Factoring and Quadratic Equations
Word Problems
The applications in this chapter will involve multiplication. Look for the keyword “product” which indicates that we will have to multiply in our set-up. Remember to read the question several times, identify the variables and use algebra to solve the problems. Whenever possible we will try to set them up using only one variable.
A. Number Problems
One positive number is 4 less than twice another positive number and their product is 96. Set-up an algebraic equation and solve it to find the two numbers.
The difference between two positive integers is 5 and their product is 126. Find the two integers.
Sarah is 2 years older than her brother Ryan. If the product of their ages is 15 how old are they. ( Set up an algebraic equation and solve it )
Consecutive integers and consecutive even and odd integer problems pretty much always show up on the final exam. We need to be comfortable with them. Recall that consecutive integers are separated by 1 and consecutive even and odds are separated by 2 units.
B. Consecutive Integer Problems
Basic Guidelines for Solving Word Problems :
The product of two consecutive odd positive integers is 99. Find the integers.
The product of two consecutive even positive integers is 168. Find the integers
The product of two consecutive integers is 182. Find the integers.
Since this problem did not specify negative or positive integers we must provide both answers.
Notice that the set- up is the same as odds.
_1. Read the problem several times and organize the given information.
- Identify the variables by assigning a letter to the unknown quantity.
- Set up an algebraic equation.
- Solve the equation.
- Finally, answer the question and make sure it makes sense._
Pythagorean Theorem – For any right triangle with hypotenuse c and legs a and b.
a^2 + b^2 = c^2
The height of a triangle is 3in less than twice the length of its base. If the total area of the triangle is 52 in^2 find the lengths of the base and height.
The hypotenuse of a right triangle is 2cm more than the smallest leg. If the other leg measures 4cm find the lengths of the other two sides.
The hypotenuse of a right triangle measures 10 in. If the small leg is 2in less than the longer leg, find the lengths of the legs.
Hypotenuse measures x + 2 = 8 + 2 = 10cm
For the following projectile problems we will use the formula for the height
where t is time in seconds, is the initial velocity and s is the
initial height.
h ( t )= − 16 t^2 + v 0 t + s v 0
D. Projectile Problems
A projectile is launched from a roof 80ft high at an initial velocity of 64 feet per second. How long will it take the projectile to land on the ground?
Old fashioned big caliber handguns (45 Colt, 44 S+W) shoot a heavy bullet without a lot of gun powder behind it. Muzzle velocities for these weapons average 1000 feet per second. If a handgun is shot up into the air from the ground how long will it take to bullet to come back to the ground? ( Wind and air resistance are not part of this calculation )
From the previous problem, how high is the bullet at t = 30 seconds.
