# Question #b0d8e

##### 1 Answer

#### Answer:

#### Explanation:

Your goal here is to wirte two equations with two unknowns, the **price per item**, *number of items*,

Let's say that at the **initial price** of

#P * x = 45000" " " "color(purple)((1))#

Now the price per item is **reduced** by

SInce now **25 items more**, you can say that

#P^(') * (x + 25) = 45000#

This is equivalednt to

#overbrace(90/100 * P)^(color(blue)(=P^('))) * (x+25) = 45000" " " " color(purple)((2))#

Use equation

#P = 45000/x#

and use this value in equation

#90/100 * color(red)(cancel(color(black)(45000)))/x * (x + 25) = color(red)(cancel(color(black)(45000)))#

Solve this equation for

#90/100 * 1/color(red)(cancel(color(black)(x))) * color(red)(cancel(color(black)(x))) + 90/100 * 1/x * 25 = 1#

This is equivalent to

#90x + 2250 = 100x#

#10x = 2250 implies x = 2250/10 = 225#

The **initial number of items** is thus equal to

#color(purple)((1)) implies P = 45000/225 = color(green)(200)#

So, initially you had

#90/100 * 200 = 180#

which means that you can now buy

#180 * (225 + 25) = 45000#