Question #b0d8e

1 Answer
Oct 21, 2015

Answer:

#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#