Application Problems
The UAH bookstore is selling used textbooks at a discounted price. You decide to buy a used math textbook, and you pay a discounted price of $29.75. If the discount was 15% off, what was the original price?
x-x(.15)=29.75
How would you write this in interval notation:
-3<x<=0
(-3,0]
Factor:
x2+6x-27
x= -9, 3
Solve using Quadratic Formula:
x2+6x+12
x = -3 + i root(3)
x = -3 - i root(3)
Solve:
(3 + 2i)+(-4i + 1)
4 - 2i
You are building a fence and trying to determine what dimensions to make your fence. Your backyard has a length that is 5ft more than twice its width. What are the dimensions of your fence if the perimeter of your backyard is 255 ft.
P= 2W + 2L
P=255
L=5+2W
255=2W+2(5+2W)
Answer in interval notation:
-2 < 2x-1 < 5
(-1/2,3)
Solve using Square Root Method:
(x+1)2=4
x = 3, -1
Solve using Complete the Square:
x2+10x-2
x = -5 + 3i root(3)
x = -5 - 3i root(3)
Solve:
(5+7i)-(-3-i)
8+8i
Ashley invests $20,000, some in stocks and the rest in bonds. If she invests 3 times as much in stocks as she does bonds, how much does she invest in each?
3b + b = 20,000
Answer in interval in notation:
7 <= -4x + 3 < 3
(0,-1]
Factor:
x4+20x2+64
x= 2i, -2i, 4i, -4i
Solve using Quadratic Formula:
2x2-7x+13
x = (7/4) + i root(3)
x = (7/4) - i root(3)
Solve:
(1+3i)(-2-i)
-7i + 1
Two twin sisters took turns washing their car on the weekends. Grace can wash their car in 45 minutes and Joann can wash their car in 30 minutes. One weekend, they decide to wash the car together. How long will it take them to wash their car?
x/45 + x/30 = 1
Answer in interval notation:
4 | (x/9) | + 7 >= 11
(-infinity, -9]U[9, infinity)
Solve using Square Root Method:
(x2+2)2=9
x= -1, 1, root(-5), -root(-5)
Solve using complete the square:
x2-6x-9=0
x = 3 + 3 root2
x = 3 - 3 root2
Solve (-2i+5)(4i+1)
18i + 13
How many gallons of 40% sulfuric acid solution should be mixed with 20% sulfuric acid solution to obtain 50 gallons of 25% sulfuric acid solution?
(.40)(x) + (.20)(50-x) = (.25)(50)
Answer in interval notation:
6 | x - 5 | + 6 >= -84
(- infinity, infinity)
Solve the rational expression:
(1/x) + (x/x+3) = (2x/x)
x = -5/2 + root (37)/2
x = -5/2 - root(37)/2
Solve the rational expression:
(1/x-4) + (x/x+1) = (-1/x2-3x-4)
x= 1,2
Solve:
(1+2i) / (4-2i)
i/2