Photography reprints cost $0.52 each at a local photo shop. Through the mail, they cost $0.44 each plus $1.20 postage and handling. How many reprints must a customer purchase to make it less expensive to use mail order?
you have two functions:
cost1 = .52x
cost2 = .44x + 1.2 , where x is the number of prints
the costs are equal when
cost 1 = cost2 , or
.52x = .44x + 1.2
solving this you get x = 15
so try 16 in each equation to see which is the cheaper.
So basically the answer would be x>15? Does this make sense considering that 16 is greater than 15? Thanks for the help!
yes, you got it
Thanks! Take care! :)
To determine when it is less expensive to use mail order, we need to compare the total cost of purchasing reprints at the local photo shop with the total cost of purchasing reprints through mail order.
Let's assume the customer needs to purchase "x" reprints.
Cost at the local photo shop:
Total cost = cost per reprint x number of reprints
Total cost = $0.52 * x
Cost through mail order:
Total cost = (cost per reprint + postage and handling) x number of reprints
Total cost = ($0.44 + $1.20) * x
To find when it is less expensive to use mail order, we need to find the value of "x" when the total cost through mail order is less than the total cost at the local photo shop.
($0.44 + $1.20) * x < $0.52 * x
Simplifying the inequality:
$1.64x < $0.52x
Dividing both sides by x (since x > 0):
$1.64 < $0.52
Since the value on the left side is higher than the value on the right side, this inequality is always false.
Therefore, it is never less expensive to use mail order. Regardless of the number of reprints a customer purchases, it will always be more expensive to use mail order compared to purchasing reprints at the local photo shop.