GeminiHeat wrote:
A computer company prices its models using the formula \(P = 1.25^sa\), where P is the price per unit, a is a constant, and s is the speed rating, from 1 to 20, of the product. The company also grants a discount of 10% on orders of 100 to 249 units and a discount of 25% on orders of 250 or more units. Lotte orders 300 computers, all with the same speed rating. How many computers could she have purchased for the same price if she had chosen models with a speed rating 2 higher than the ones she chose?
A) 160
B) 192
C) 230
D) 240
E) 675
Since Lotte ordered 300 computers, he must get a 25% discount
Price for 1 computer with speed rating \(s\) = \(1.25^sa\)
Price for 1 computer with speed rating \(s+2\) = \(1.25^{s+2}a\)
Price for 300 computers with speed rating \(s\)= \(0.75(300P) = (225)1.25^sa\)
Now, the question is - how many computers (let it be \(n\)) could she have purchased for the same price and with a speed rating 2 higher
Note here, all the option choices are above 100 - so he must get a discount of at-least 10%
i.e. \((n)(0.90)1.25^{s+2}a = (225)1.25^sa\)
\(n = \frac{(225)1.25^sa}{(0.90)1.25^{s+2}a} = \frac{(225)(1.25^s)(a)}{(0.90)(1.25^s)(1.25^2)(a)} = \frac{225}{(0.90)1.25^2} = \frac{225}{1.40625} = 160\)
We have a match, Hence option A