Probability and Algebra Example word problems

 
PROBABILITY:

QUESTION: 23
Keisha is playing a game using a wheel divided into eight equal sectors as shown in the diagram below each time the spinner lands on orange she will win a prize. If Keisha spins the wheel twice what is the probablity she will win a prize on both spins.

 

 
W- White
O - Orange
Br - Brown
Y - Yellow
G - Green.
Bl - Blue.

 
Solution:

 
The Probability of winning a prize is:

 
Outcome favourable to the event
= ---------------------------------------
Total number of outcomes

 

 
= 1/8 + 1/8 = 2/8
= ¼

 

 
ALGEBRA I
QUESTION : 24

 
Divide the rational expressions:

 
3x+6 x^2 - 4
------- ---------
4x+12 x+3

 
Solution:

 
Factor each expression


 
3x+6 take out 3 as the common factor. So, 3(x+2)

 
4x+12 take out 4 as the common factor. So, 4(x+3)

 
X^2 -4 = x^2 - 2^2

 
Using the identity a^2-b^2 = (a+b)(a-b)

 
Factor x^2- 2^2 = (x+2)(x-2)

 
Apply all these factor form in the place of it's expression

 
Then the rational division is just inversing the denominator and multiply
With the numerator

 

 

 
3(x+2) x+3
------- * -----------
4(x+3) (x+2)(x-2)

 
Solve this, we will get

3
-------
4(x-2) as solution.

 

 
ALGEBRA I
QUESTION:25.

 
The price per person to rent a limo for a prom varies inversely as the number of passengers. If 5 people rent a limo, the cost is $70 each. How many People are renting the limo when the cost per couple is $87.5.

 

 
Solution:

 
Rent per person cost
x              y

 
5             $70
x2              $87.5

 
Here, x2 represent number of couples. From the problem it uses inverse variation formula here,

 
x1 y2
--- = --
x2 y1

 
5 87.5
-- = ------ [ cross multiply, solve for x2]
x2 70

 
x2 = 4

 
Rent for 4 couples is $87.5.