Question

Four hundred gallons of 89-octane gasoline is obtained by mixing 87-octane gasoline with 92-octane gasoline.

(a)
Write a system of equations in which one equation represents the total amount of final mixture required and the other represents the amounts of 87- and 92-octane gasoline in the final mixture. Let x and y represent the numbers of gallons of 87-octane and 92-octane gasolines, respectively.
amount of final mixture required
amounts of 87- and 92-octane gasolines in the final mixture
(b)
Use a graphing utility to graph the two equations in part (a) in the same viewing window. As the amount of 87-octane gasoline increases, how does the amount of 92-octane gasoline change?
There is not enough information given.
As the amount of 87-octane gasoline increases, the amount of 92-octane gasoline stays the same.
As the amount of 87-octane gasoline increases, the amount of 92-octane gasoline increases.
As the amount of 87-octane gasoline increases, the amount of 92-octane gasoline decreases.
As the amount of 87-octane gasoline increases, the amount of 92-octane gasoline fluctuates.
(c)
How much (in gallons) of each type of gasoline is required to obtain the 400 gallons of 89-octane gasoline?
87-octane gal
92-octane gal

Answer 1

a) The total volume equals the sum of the volumes.

`500 = x + y`

The total octane amount equals the sum of the octane amounts.

`89(500) = 87x + 92y`

`44500 = 87x + 92y`

b)

As x increases, y decreases.

c) Use substitution or elimination to solve the system of equations.

`44500 = 87x + 92(500-x)`

`44500 = 87x + 46000 - 92x`

`5x = 1500`

`x = 300`

`y = 200`

The required volumes are 300 gallons of 87 gasoline and 200 gallons of 92 gasoline.