Task 5 PROBABILITY, STATISTICS, & QUANTITATIVE PROBLEM - Essay Example

Task A A is looking for the best option in purchasing school supplies. Company A is offering a discount of 10% for every dollar amount spent;Company B is offering a higherdiscount of 20%, but the discount is only applicable after a $20minimum is spent on supplies.The student is looking for the company that will save her the most amount of money overall. Given that she is on a fixed income it will be important for her to receive the highest amount of savings when she purchases school supplies.

It needs to be determined which company would save the student the most amount of money.There are two options for the student to consider: Firstoption is to purchase from company A, assuming it offers a discount of 10% on each dollar spent.Second option is to purchase from company B, assuming it offers a discount of 20%, but it’s only gained if a dollar is spent on top of $20Task BIn this case let y is the amount of purchases from company B x is the amount spend in purchasing from company ACompany A;Let the discount be represented by x, it represents the cost subsequent to discount.

Then equationsrelatingCompany A: X= 0.90xCompany B; Let the discount be represented by y, it represents the cost subsequent to discount.Then equations relating Company B:y20, y=0.80y +4 given y>20Company A: Let the cost prior to discount be represented by x. Company A offers a discount of 10%. 10% of x is the discount. It is derived at by product of x and 10/100(0.1).Therefore 0.1x is the discount. The cost subsequent to discount is arrived at by deducting discount from cost subsequent to discount.

Therefore cost subsequent to discount is x-0.1x=0.9x. Hence the cost before and after tax is X=0.9x.Company B; let the cost prior to discount be represented by y. Company B wont award discount if y≤20. Hence cost subsequent to discount is y. We end up with the equation y= given y≤20. Incase y exceeds 20, company B will award 20% discount for any amount more than 20 dollars. The amount more than 20 dollars is y-20.discount is 20/100 of (y-20) =0.2x-4. The cost y subsequent to discount is given by 0.8x+4. Hence the cost before and after tax is connected by y=x given x≤20, y=0.

8x+4 given y>20Company A: The cost prior to discount is not more than 20 dollars. Systems of equations to be solved are x=0.9x, y=x and y=y .it implies that x=y=y. therefore x=0.9x hence dividing both sides by x we get 0.hence solution to the systems is x=o, y=0 and z=0. It implies that incase purchases are more than 20dollars, the two companies’ offers are equal if they do not purchase at all. Incase x inclines from 0 to 20 company’s A offer is better as they give10% discount and no discount is given by company B.

Company B: The cost prior to discount is more than 20 dollars. Systems of equations to be solved are y=0.9x, y=0.8x+4 and y=y meaning 0.9x=0.8x+4 which gives us 0.1x=4 hence x=40. Y=0.9×40=36 and y=y=36. The solutions to this system is therefore x=40, y=36 and y=36. It implies that incase purchases are more than 20dollars, the two companies’ offers are equal if the amount prior to discount is 40dollars.if 20