Question 834950: an incentive amount of rs 58000 was divided among three sales persons (lovleen, ankita, and arun). lovleen got 80 percentage of what ankita got and 25 percentage of what arun got. find the amount that each sales person got. also find what percentage of the incentive amount that ankita received. kindly give its step also.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the total incentive was 58000.
let x represent the amount that lovleen got.
let y represent the amount that ankita got.
let z represent the amount that arun got.
first equation you get is:
x + y + z = 58000
lovleen got 80% of what ankita got.
this translates to x = .8y
lovleen got 25% of what arun got.
this translates to x = .25z
since you have x = .8y and also x = .25z, this means that:
.8y = .25z
if you solve for y in this equation, you get:
y = .25z/.8 which becomes:
y = .3125z
you now have some equalities that will allow you to make your original equation of:
x + y + z = 58000
in terms of one of the variables only.
that variable will be z.
your equalities are:
x = .25z
y = .3125z
you can now express your original equation in terms of z by replacing x with .25z and by replacing y with .3125z to get:
.25z + .3125z + z = 58000
you can now solve for z.
combine like terms on the left side of the equation to get:
1.5625z = 58000
divide both sides of the equation by 1.5625 to get:
z = 58000 / 1.5625 = 37120
now that you know the value of z, you can easily find the values for x and y.
you already know that x = .25z, so x must be equal to 9280.
you already know that y = .3125z, so y must be equal to 11600.
your answers are:
x = 9280
y = 11600
z = 37120
now all you have to do is confirm the solutions are correct.
x + y + z = 58000 becomes:
9280 + 11600 + 37120 = 58000 which becomesL
58000 = 58000 so that part is correct.
x must be 80% of y.
9280 / 11600 = .8 which is 80% so that part is correct.
x must be 25% of z.
9280 / 37120 = .25 which is 25% so that part is correct.
all parts are correct so the solution is good.
you could also have solved this by treating it as 3 equations that needed to be solved simultaneously.
the first equation would be:
x + y + z = 58000
the second equation would be x = .8y which you would translate to x - .8y = 0
the third equation would be x = .25z which you would translate to x - .25z = 0
your three equations would be:
x + y + z = 58000
x - .8y = 0
x - .25z = 0
you would fill in the missing terms to get:
x + y + z = 58000
x - .8y + 0z = 0
x + 0y - .25z = 0
this can be solved by substitution or by elimination.
all 3 equations have to have a common solution for x and y and z.
this could also be solved by graphing since it's 3 dimensional, but graphing is very difficult to see in 3 dimensions so you probably would just opt to solve by substitution or elimination.
this could also be solved by using matrices.
it depends on how advanced you are in your studies whether you would solve by matrix or not.
the method i used was similar to substitution.
i solved for all veriables in terms of one variable (z) and was then able to solve for z.
once i did that, the rest was easy.
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