Question

one tamk of gasoline has an octane rating of 140 and another tank of gasoline has an octane rating of 80. To obtain a mixture of 60 gallons with an octane rating of 120, how many gallons should be used from the tank with the octane rating of 80?

Answer 1

20 gallons were used from the tank with the octane rating of 80.

Explanation:

Given : One tank of gasoline has an octane rating of 140 and another tank of gasoline has an octane rating of 80. To obtain a mixture of 60 gallons with an octane rating of 120.

To find : How many gallons should be used from the tank with the octane rating of 80?

Solution : Let x be the volume of gas whose octane rating is 140 and

y be the volume of gas whose octane rating is 80.

Then, we form the equation as:

(1)
`x*140 + y*80 = 60*120`

`140x+80y = 7200`

or
`7x+4y = 360` .........[3]

(2)
`x + y = 60`

Now multiply equation (2) by 4

`4x + 4y = 240` ...........[4]

Subtract (4) from (3)

`7x+4y-4x-4y=360-240`

`3x=120`

`x=(120)/(3)`

`x=40`

Put x in equation [4] we get,

`4(40) + 4y = 240`

`160 + 4y = 240`

`4y = 80`

`y=(80)/(4)`

`y=20`

Therefore, x=40 and y=20

So, 20 gallons were used from the tank with the octane rating of 80.