Question 947570: Person A, B and C work together under a contract. The compensation is divided in relation to their working hours. The relation of the working hours of A and B is 2:3 and that of B and C correspondingly 4:5. How many Euros was the share of A, when the whole amount to be divided was 1400 Euros?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let a represent the number of hours that A worked.
let b represent the number of hours that B worked.
let c represent the number of hours that C worked.
the ratio of a to b is equal to 2 to 3.
the ratio of b to c is equal to 4 to 5.
mathematically this may be expressed as:
a/b = 2/3 and b/c = 4/5
since they are being paid in the same proportion as the hours that they worked, then a,b,c can also represent the amount of money that each made.
since the total amount is 1400 euro, then a + b + c must be equal to 1400.
one way to solve this is to make everything in terms of one of the variables.
we'll make everything in terms of b.
you know that a/b = 2/3.
solve for a to get a = 2b/3.
you know that b/c = 4/5.
solve for c to get c = 5b/4.
you now have a and c valued in terms of b.
you have:
a = 2b/3
b = b
c = 5b/4
in the equation of a + b + c = 1400, replace a with 2b/3 and replace c with 5b/4 to get:
2b/3 + b + 5b/4 = 1400
multiply both sides of this equation by 12 to get 8b + 12b + 15b = 16800
combine like terms to get 35b = 16800
solve for b to get b = 480
if b = 480, then a = 2*480/3 and c = 5*480/4
simplify these equations and you get:
a = 320
b = 480
c = 600
a + b + c = 1400 becomes 320 + 480 + 600 = 1400 which becomes 1400 = 1400 which is true.
a/b = 2/3 becomes 320/480 = 2/3.
cross multiply to get 3*320 = 2*480 which becomes 960 = 960 which means that the ratios are equivalent.
b/c = 4/5 becomes 480/600 = 4/5
cross multiply to get 5*480 = 4*600 which becomes 2400 = 2400 which mean that the ratios are equivalent.
all the numbers check out.
your solution is that the share of A is equal to 320 euros.
|
|
|
