Problema Solution
a chemical manufacturer wants to lease a fleet of 24 railroad tank cars with a combined carry8ing capacity of 520,000 gallons. Tank cars with three different carrying capacities are available: 8,000 gallons, 16,000 gallons, 24,000 gallons. The cost of leasing an 8,000 gallon car is $450 per month, a 16,000 gallon tank car is $650 per month, and a 24,000 gallon tank car is $1,150 per month. If the company spends a total of 25,000 per month on tank car leases, how many of each type of tank car do they lease?
Answer provided by our tutors
let
x = the number of 8,000 gallon cars
y = the number of 16,000 gallon cars
z = the number of 24,000 gallon cars
a chemical manufacturer wants to lease a fleet of 24 railroad tank cars:
x + y + z = 24
with a combined carry8ing capacity of 520,000 gallons:
8000x + 16000y + 24000z = 520000 divide both sides by 8000
x + 2y + 3z = 65
the company spends a total of 25,000 per month on tank car leases:
450x + 650y + 1150z = 25000 divide both sides by 50
9x + 13y + 23z = 500
by solving the system of equations
x + y + z = 24
x + 2y + 3z = 65
9x + 13y + 23z = 500
we find
x = 3 cars
y = 1 cars
z = 20 cars
click here to see the step by step solution of the system of equations
they lease 3 cars of 8,000 gallons, 1 car of 16,000 gallons and 20 cars of 24,000 gallons.