Question #b0d8e

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Answer 1 · 2015-10-21T15:28:09

$200$

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

$180 * (225 + 25) = 45000$