tman244 wrote:Jellow! Need some help with the question below. What is the easiest way to solve this:

If an item that originally sold for z dollars was marked up by x percent and then discounted by y percent, which of the following expressions represents the final price of the item?

10,000z + 100z(x – y) – xyz
10,000

10,000z + 100z(y – x) – xyz
10,000

100z(x – y) – xyz
10,000

(100z(y – x) – xyz)
10,000

10,000
100yz + xy

Thank you for everyones insight

I would go for A

The equation built would be,

[z+(xz/100)] - (y/100)[z+(xz/100)]

= [(100z+xz)/100)] - [(zy/100)+(xyz/10000)]
= [(100z+xz)/100)] - [(100zy+xyz)/10000]
= [10000z+100xz - 100zy-xyz]/10000
= [10000z +100z(x-y)-xyz]/10000

Answer A

One way to approach. I find it more intutive

Lets take the case of two variables first and then extend it to three.

what is the final value when z is increased by x percent?

new value = original value + increase

increase = zx/100

nv = z + zx/100

If we represent this in the form of a function,

percentinc(a, b) = a + ab/100

similary when z is decreased by y percent

nv = z - zy/100

percentdec(a, b) = a - ab/100

Now we can apply the same for three variables by extending this formula. For the given problem we can represent this as

percentdec(precentinc(z, x), y)

percentdec(z + zx/100, y)

= z + zx/100 - zy/100 - zxy/10000

only A matches the value above so the answer is A. Hope it helps

or

[z+xz/100][1-y/100]

=a