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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?

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Answer:

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.






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