SOLUTION: You need a total of 50 pounds of two types of ground beef costing $1.25 and $1.60 per pound, respectively. A model for the total cost y of the two types of beef is y = 1.25x + 1

Algebra ->  Trigonometry-basics -> SOLUTION: You need a total of 50 pounds of two types of ground beef costing $1.25 and $1.60 per pound, respectively. A model for the total cost y of the two types of beef is y = 1.25x + 1      Log On


   

Question 624012: You need a total of 50 pounds of two types of ground beef costing $1.25 and $1.60 per pound, respectively. A model for the total cost y of the two types of beef is
y = 1.25x + 1.60(50 - x)
where x is the number of pounds of the less expensive ground beef.
a) Find the inverse function of the cost function. What does each variable represent in the inverse function?
b) Use the context of the problem to determine the domain of the inverse function.
c) Determine the number of pounds of the less expensive ground beef purchased when the total cost is $73
(I have tried A and B, A. (x-80)/-0.35=y x=total cost, y=number of pounds
B.y=all real numbers)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You have good answers for parts a) and b).
I would write the inverse as
y=%2880-x%29%2F0.35 or y=-%2820%2F7%29x%2B1600%2F7
but that is just my bias (because I do not like negative numbers in denominators).
As you said (or meant to say), in the inverse function, x is the cost per pound for the mixed ground beef, and y is the number of pounds of the less expensive ground beef.
(Do not forget to specify what's your beef, for which the y in the inverse function represents the number of pounds).
c) y%2873%29=%2880-73%29%2F0.35=7%2F0.35=20 is the number of pounds of the less expensive ground beef that must be in the mix to get 50 pounds of a mix with a total cost of x=$73.
Of course, 30 pounds (50 pounds - 20 pounds = 30 pounds) of that mix will be the more expensive ground beef.