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

Answer:

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

Step-by-step 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) $x\times140 + y\times80 = 60\times120$

$140x+80y = 7200$

or  $7x+4y = 360$ .........[3]

(2) $x + y = 60$

Now multiply equation (2) by 4  

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

Subtract (4) from (3)  

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

$3x=120$

$x=\frac{120}{3}$

$x=40$

Put x in equation [4] we get,

$4(40) + 4y = 240$

$160 + 4y = 240$

$4y = 80$

$y=\frac{80}{4}$

$y=20$

Therefore, x=40 and y=20

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