Question 1081196: 1.) A shop keeper sold 2 bicycles for #1,500 each. On onevhe gains 25% and on the other he loses 20%. His gain or loss percent in the whole transaction is?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! he sells both bikes for 1500 each.
let x = the cost of the first bike.
let y = the cost of the second bike.
selling price for the first bike is 1.25 * x.
selling price for the second bike is .80 * y.
that's because x + .25 * x = 1.25 * x and because y - .20 * y = .80 * y.
1.25 * x = 1500
.80 * y = 1500
his total selling price for both bikes was 3000
1.25 * x + .80 * y = 3000
you have one equation in two unknowns.
you need to make this one equation in one unknown in order to be able to solve it.
since you kmow that both 1.25 * x and .8 * y are each equal to 1500, then you know that 1.25 * x must be equal to .8 * y
therefore, since .8 * y is equal to 1.25 * x, in the equation of 1.25 * x + .8 * y = 3000, you can replace .8 * y with 1.25 * x to get:
1.25 * x + 1.25 * x = 3000
combine like terms to get 2.5 * x = 3000
solve for x to get x = 3000 / 2.5 = 1200.
since 1.25 * x = .8 * y, and since x = 1200, you get:
1.25 * 1200 = .8 * y.
solve for y to get y = 1.25 * 1200 / .8 = 1875.
the first bike cost 1200
the second bike cost 1875.
the first bike cost 1200 and was sold for 1500 with a profit of 300 which is equal to 300 / 1200 = .25 * 100 = 25%.
the second bike cost 1875 and was sold for 1500 with a loss of 375 which is equal to 375 / 1875 = .2 * 100 = 20%.
solution looks good.
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