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galben [10]
3 years ago
6

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?
Mathematics
1 answer:
Zarrin [17]3 years ago
7 0

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.






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