The weekly revenue of a business selling gummy bear bags is a function of price. Weekly revenue is $10,816 when the price is $1.60 but is $9,344 when the price is $3.20 Find a quadratic model that fits this information. Also know that the revenue is $0 if the price is $0. Let p = the price of a bag of gummy bears. Then: Revenue = R ( p ) =

R(p) = -2400p² + 10600p

Step-by-step explanation:

p = The price of a bag of gummy bears

R(p) = Revenue

A quadratic model for the revenue R(p) can be written as:

R(p) = ap² + bp + c(1)

When R = $10,816  p = $1.60

10816 = a(1.60)² + b(1.60) + c

10816 = 2.56a + 1.6b + c(2)

When R = $9,344  p = $3.20

9344 = a(3.20)² + b(3.20) + c

9344 = 10.24a + 3.20b + c(3)

When R = $0, p = $0

0 = a(0)² + b(0) + c

c = 0

Therefore, equations (1) and (2) become:

10816 = 2.56a + 1.6b(4)

9344 = 10.24a + 3.20b(5)

From the two simultaneous equations above:

a = -2400, b = 10600

Therefore the quadratic model in equation becomes:

R(p) = -2400p² + 10600p

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

cant open file sorry!

step-by-step explanation: