SOLUTION: I have a word problem that says, "Determine whether an outfitter leading a backpacking trip would find it more cost effective to make a one time bulk purchase at a buyers club with

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: I have a word problem that says, "Determine whether an outfitter leading a backpacking trip would find it more cost effective to make a one time bulk purchase at a buyers club with      Log On


   

Question 295135: I have a word problem that says, "Determine whether an outfitter leading a backpacking trip would find it more cost effective to make a one time bulk purchase at a buyers club with membership fees or purchase the same goods at a conventional supermarket." I have to develop an algebraic equation for each option and then graph it. I believe the equations should be in the form "y=mx+b". I chose trail mix as an appropriate real world item to price compare, and found Sam's club membership fees to be 35.00, and Sam's club trail mix to cost 7.48 for a 48oz bag. I went to Walmart supercenter to compare and their biggest bag is 28 oz for 4.98. So the two equations I have are y=(4.98/28)x+o for walmart and y=(7.98/48)x+35 for Sam's club. Is this correct? I'm not sure if I'm factoring in the membership fee correctly. Thank you for taking the time to help me.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
Price at Sam's would be:

$35.00 + $7.48 per 48 ounce bag.

Price at Walmart would be:

$4.98 per 28 ounce bag.

You have 2 equations.

y = (4.98/28)*x for Walmart.

y = $35.00 + (7.48/48)*x for Sam's.

It looks like your equations are correct.

To look for a break even point, you would set these equations equal to each other.

You would get:

(4.98/28) * x = 35 + (7.48/48) * x

You would subtract (7.48/48) * x from both sides of this equation to get:

(4.98/28) * x - (7.48/48) * x = 35

You would factor out the x to get:

x * (4.98/28) - (7.48/48) = 35

You would divide 4.98/28 to get the cost per ounce, and you would divide 7.48/48 to get the cost per ounce.

You would get:

x * (.177857143 - .155833333) = 35

You would combine like terms to get:

x * (.02202381) = 35

You would divide both sides of this equation by .02202381 to get:

x = 1589.189189 ounces.

That's you break even point.

To confirm, you would substitute in your original equation to get:

(4.98/28) * x = 35 + (7.48/48) * x would become:

(4.98/28) * 1589.189189 = 35 + (7.48/48) * 1589.189189 which would become:

282.6486486 = 282.6486486 confirming that the value for x is good.

Your answer would be:

At less than 1589.189189 ounces, it would be cheaper to go to Walmart.

At greater than 1589.189189 ounces, it would be cheaper to to to Sam's.