A lady purchased one piece of cloth for 1600 rupees .Had the price rate of cloth been 40 rupees per metre less, then she would have purchased 2 metre cloth more in the same amount.Find the measure of cloth and price per metre.
Answers
Answer:
let x = the price per meter.
let y = the number of meters.
you start with x * y = 1600
that means that the number of meters of cloth times the price per meter equals the total cost of the cloth.
you state that, if the price of the cloth per meter was 40 less, then she would be able to purchase twice as much cloth for the same price.
the formula for that would be:
(x-40) * 2y = 1600
you have two equations that need to be solved simultaneously.
they are:
xy = 1600
(x-40)*2y = 1600
they have to be solved simultaneously because the values of x and y have to be the same for both equations.
if you divide both sides of the second equation by 2, you will get:
xy = 1600
(x-40)y = 800
solve for y in terms of x in the first equation to get y = 1600/x.
replace y in the second equation with 1600/x to get (x-40) * 1600/x = 800.
multiply both sides of this equation by x to get (x-40) * 1600 = 800x.
distribute the multiplication to get 1600x - 40*1600 = 800x.
subtract 800x from both sides of the equation and add 40*1600 to both sides of the equation to get 1600x - 800x = 40*1600
combine like terms and simplify to get 800x = 64000
divide both sides of the equation by 800 to get x = 64000/800 = 640/8 = 80.
when x = 80, xy = 1600 becomes 80y = 1600
solve for y to get y = 1600/80 = 160/8 = 20
you have x = 80 and y = 20
this means that the cost per meter is 80 and the number of meters is 20 for a total cost of 80 * 20 = 1600.
if you subtract 40 from the cost per meter, you get x = 40.
if you double the number of meters, you get 20 * 2 = 40.
total cost is then the same at 40 * 40 = 1600.
your solution is that the cost per meter of the cloth is 80 and the number of meters is 20. ****