Problema Solution
Three roommates share the cost of a $300 television. The first pays a half of the total amount paid by the second and third roommates. The second roommate pays a third of the total amount paid by the first and third roommates.
How much does the third roommate pay towards the television
Answer provided by our tutors
let
x = the amount that the first roommate pays
y = the amount that the second roommate pays
z = the amount that the third roommate pays
three roommates share the cost of a $300 television
x + y + z = 300
the first pays a half of the total amount paid by the second and third roommates
x = (1/2)(y + z)
the second roommate pays a third of the total amount paid by the first and third roommates
y = (1/3)(x + z)
by solving the system of equations
x + y + z = 300
x = (1/2)(y + z)
y = (1/3)(x + z)
we find
x = $100
y = $75
z = $125
click here to see the step by step solution of the system of equations
the third roommate pays $125.