Question 899335
last month mrs santos bought x kilos of fish for 600 today she paid the same amount but got 3 kilos less due to price increase of 45 per kilo. Find the value of x and the original price of a kilo of fish?


Thank you please help.
<pre>
Amount purchased last month: x kilos
Since last month, she bought x kilos for 600, she paid {{{600/x}}}, per kilo, then 
Since today, she bought x – 3 kilos for 600, she paid {{{600/(x - 3)}}}, per kilo
Since there was a 45 per kilo increase, then we have: {{{600/x + 45 = 600/(x - 3)}}}
600(x – 3) + 45(x)(x - 3) = 600(x) ------- Multiplying by LCD, x(x – 3)
{{{600x - 1800 + 45x^2 - 135x = 600x }}}
{{{45x^2 - 600x + 600x - 135x - 1800 = 0}}}
{{{45x^2 - 135x - 1800 = 0}}}
{{{45(x^2 - 3x - 40) = 45(0)}}} ------ Factoring out GCF, 45 
{{{x^2 - 3x - 40 = 0}}}
(x - 8)(x + 5) = 0 
x, or original amount purchased = {{{highlight_green(8)}}} kilos		OR		x = - 5 (ignore)
Original price of 1 kilo: {{{600/8}}}, or {{{highlight_green(75)}}}
You can do the check!! 

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