You pay $24.50 for 10 gallons of gasoline and 1 quart of oil at a gas station. Your friend pays $22 for 8 gallons of the same gasoline and 2 quarts of the same oil. Find the cost of a quart of oil and a gallon of gas.

the cost of a quart of oil and a gallon of gas is $2 and $2.25 respectively

Step-by-step explanation:

The computation of the cost of the quart of oil and the gallon of gas is as follows:

Let us assume the gallons of gasoline be x

And, the quart of oil be y

Now

As per the question

10x + y = $24.50 (i)

8x + 2y = $22 (ii)

Now divide by 2 in equation 2

4x + y = $11

y = $11 - 4x

Now put the value of y in any of the equation

10x + $11 - 4x = $24.50

6x = $24.50 - $11

6x = $13.5

x = $2.25

And, y

= $11 - 4(2.25)

= $2

Hence, the cost of a quart of oil and a gallon of gas is $2 and $2.25 respectively

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

step-by-step explanation:

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