Question

Question #b0d8e

Answer 1

`200`

Explanation:

Your goal here is to wirte two equations with two unknowns, the price per item, `P`, and the number of items, `x`.

Let's say that at the initial price of `P` you were able to buy a total of `x` items for `45000`. This means that you can write

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

Now the price per item is reduced by `10%`. This is equivalent to saying that the new price, `P^(')`, is equal to `90%` of the old price.

SInce now `45000` can buy you 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 `color(purple)((1))` to find

`P = 45000/x`

and use this value in equation `color(purple)((2))` to get

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

Solve this equation for `x` to get

`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 `225`. This means that the initial price per item was

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

So, initially you had `225` items at `200` each. The price decreased by `10%` to

`90/100 * 200 = 180`

which means that you can now buy `250` items, `25` more thn you had initially

`180 * (225 + 25) = 45000`