Problema Solution
A company that rents small moving trucks wants to purchase 25 trucks with a combined capacity of 28, 000 cubic feet. Three types of trucks are a available: a 10-ft truck with a capacity of 350 cubic feet, a 14-foot truck with a capacity of 700 cubic feet, and a 24 foot truck with a capacity of 1400 cubic feet. How many trucks of each should be purchased (general solution)? How many trucks of each if 16 24-foot trucks are purchased?
Answer provided by our tutors
Let
x = the number of 10-ft truck with a capacity of 350 cubic feet
y = the number of 14-ft truck with a capacity of 700 cubic feet
z = the number of 24-ft truck with a capacity of 1400 cubic feet
x + y + z = 25
350x + 700y + 1400z = 28000
........
click here to see the system of equations solved for x and y
........
x = 2z - 30
y = -3z + 55
If the number of 24-ft trucks is 16 we have z = 16 and plug the value into the solution:
x = 2*16 - 30
x = 2 10-ft trucks
y = -3*16 + 55
y = -48 + 55
y = 7 14-ft trucks
There are two 10-ft and seven 14-ft trucks purchased.