Math Help - Algebra expressions problem

1. Algebra expressions problem

Hi, I's reviewing my algebra skills for my economics program. i need some help with the following question:

Q: A good costs a basic $180 a unit but if an order is made for more than 10 units this price is reduced by a discount of$2 for every one unit increase in the size of an order (up to a maximum of 60 units purchased), i.e. if the order size is 11, price is $178, it is is 12, price is$176 etc. Write an expression for the total cost of an order in terms of order size and simplify it. Assume order size is between 10 and 60 units.

Any help would be greatly appreciated.
Thanks

2. Helolo, dragonation!

A good costs a basic $180 a unit, but if an order is made for more than 10 units, this price is reduced by a discount of$2 for every unit increase in the size of an order.
That is, if the order size is 11, price is $178; if it is 12, price is$176, etc.

Write an expression for the total cost of an order in terms of order size and simplify it.
Assume order size is between 10 and 60 units.

Let $x$ = number of units in the order over 10.

The number of units in the order is: . $10 + x$

For each $x$, there is a \$2 disccount on the unit price.
That is, for each $x$ over 10, the price is reduced by $2x$ dollars.

For $(10+x)$ units, the unit price is: . $(180 - 2x)$ dollars.

The cost of $(10+x)$ units at $(180-2x)$ dollars each is:

. . $C \;=\;(10+x)(180-2x)$

Therefore: . $C \;=\;1800 + 160x - 2x^2\;\;\;\text{ for }0 \leq x \leq 50$

3. Thanks

Thanks a lot dude. That was a lot of help. i really liked how you tackled it. Makes a lot of sense to me. More sense than the book's answer. The books answer is 200q-2q^2. Your answer looks more convincing to me since thats something close to what i got.
thanks,
dragonation

4. Hello,

Let q=quantity i.e $q>10$

Cost per unit $= 180-2(q-10)$

So total cost $= q(180-2(q-10)) = 200q-2q^2$

Hence it confirms the answer of the book!!

5. Thanks a ton buddy.