HELP!!!
A chemical manufacturer wants to lease a fleet of 26 railroad tank cars with a combined carrying capacity of 560,000 gallons. Tank cars with three different carrying capacities are​ available: 7,000 ​gallons, 14,000 ​gallons, and 28,000 gallons. How many of each type of tank car should be​ leased?

Answer:

16 of the 28,000 gallon tanks

6 of the 14,000 gallon tanks

4 of the 7000 gallon tanks

Step-by-step explanation:

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The tank should be leased by each quantity by 4 tank cars of  7000 gallons , 6 tank cars of 14000 gallons and 16 tank cars of 28000 gallons .

In the elimination method, we eliminate any one of the variables by using basic arithmetic operations and then simplify the equation to find the value of the other variable. Then we can put that value in any of the equations to find the value of the variable eliminated.

According to the question

Let Tank cars of 7000  ​gallons = x

Let Tank cars of 14000  ​gallons = y

Let Tank cars of 28000  ​gallons = z

A chemical manufacturer wants to lease a fleet of 26 railroad tank cars with a combined carrying capacity of 560,000 gallons.

i.e ,

x + y + z = 26 ---------------------------------------(1)

and

7000x + 14000y + 28000z = 560000  

x + 2y + 4z = 80  --------------------------------(2)

Now , solving equation (1) and (2) by elimination method

x = 4

y = 6

z = 16

Hence, The tank should be leased by each quantity by 4 tank cars of  7000 gallons , 6 tank cars of 14000 gallons and 16 tank cars of 28000 gallons .

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