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Crypto Maniac

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1. The length of a rectangle floor is 5 m longer than its width. The area of the floor is 84 m^2. What is the width of the floor? how about its length?


2. A Store sells lecture notes, and the monthly revenue, R of this store can be modeled by the function R(x)=3000 + 500x - 100x^2, where is X is the peso increase over Php 4. What is the maximum revenue.

NEED NG MAGANDANG FORMULA AT EXPLANATION
 
Let:
x be the width, and
x + 5 be the length

A = l x w
84 = (x + 5)(x)
84 = x² + 5x
x² + 5x - 84 = 0
(x + 12)(x - 7) = 0
x + 12 = 0
x - 7 = 0
x = -12
x = 7

We can't consider the -12, since there's no measure such as negative. Therefore, we will consider 7 only as the answer.
W = x = 7m
L = x + 5 = 7 + 5 = 12m

Check:
A = l x w
84m² = 12m x 7m
84m² = 84m²
 
2. A Store sells lecture notes, and the monthly revenue, R of this store can be modeled by the function R(x)=3000 + 500x - 100x^2, where is X is the peso increase over Php 4. What is the maximum revenue.

R(x) = -100x^2+500x+3000

b= 500

a= -100

-b/2a= -500/ -200
= 2.5

R (2.5) = -625+1250+3000
= 3,625
 
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