SOLUTION: A photo shop has a self service photo center that allows you to make prints of pictures. Each sheet of printed pictures costs $8. One sheet has four 3x5 pictures and the other sh

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: A photo shop has a self service photo center that allows you to make prints of pictures. Each sheet of printed pictures costs $8. One sheet has four 3x5 pictures and the other sh      Log On


   

Question 117380This question is from textbook Algegra I
: A photo shop has a self service photo center that allows you to make prints of pictures. Each sheet of printed pictures costs $8. One sheet has four 3x5 pictures and the other sheet has two 4x6 pictures. You want at least 16 pictures of any size and you are willing to spend up to $48. Write a system of inequalities that models the situation. Please help! Thanks. This question is from textbook Algegra I

Found 2 solutions by kamallohia, Edwin McCravy:
Answer by kamallohia(18) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the number of sheets having 4 photoes of size 3*5
and y be the number of sheets having 2 pictures of size 4*6.
Now 4x + 2y >=16
and 8(x+y)<=48

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

Warning! Kamallohia's answer omits
two trivial but important inequalities!
`
Solution by Edwin:

A photo shop has a self service photo center that allows you to make prints of pictures. Each sheet of printed pictures costs $8. One sheet has four 3x5 pictures and the other sheet has two 4x6 pictures. You want at least 16 pictures of any size and you are willing to spend up to $48. Write a system of inequalities that models the situation. Please help! Thanks.

Let x = the number of sheets of four 3x5's
Let y = the number of sheets of two sx6's

So, since the x sheets will give 4x pictures,
and the y sheets will give 2y pictures, both
together will give 4x + 2y pictures.

Also, since

>>......Each sheet of printed pictures costs $8,......<<

and there are x + y sheets, the total cost is 8(x + y)

>>......You want at least 16 pictures of any size......<<

So

4x + 2y > 16

>>......you are willing to spend up to $48......<<

So since total cost = 8(x + y),

8(x + y) < 48 

You also know that the number of sheets cannot be a
negative number but can be 0, you have these two
inequalities:

x > 0 and y > 0

So here is the system of linear inequalities which
models the situation:

4x + 2y > 16
8(x + y) < 48
x > 0
y > 0

Edwin