How to solve this using rational equations

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

Zarrin [17]

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.

7 0

3 years ago

6. Write an equation of a line that is Parallel to the line: y = 3x -3

jeka94

Answer:

3x - y -6 = 0

Step-by-step explanation:

We need to find the Equation of the line parallel to the given equation of line . The given equation of the line is ,

$\rm\implies y = 3x - 3$

Slope Intercept Form :-

$\rm\implies y = mx + c$

where ,

m is slope
c is y intercept .

Therefore , the Slope of the line is 3 . Let the parallel line passes through ( 3,3) . We know that the parallel lines have same slope . Therefore the slope of the parallel line will also be 3 .

Using point slope form :-

$\rm\implies y - y_1 = m ( x - x_1) \\\\\rm\implies y - 3 = 3( x - 3 ) \\\\\rm\implies y -3 = 3x -9 \\\\\rm\implies 3x -y -9+3=0\\\\\rm\implies \boxed{\rm\red{ 3x -y -6=0}}$

3 0

3 years ago

At a zoo, youth tickets cost $5 and adult tickets cost $9. A group that purchased x youth tickets and y adult tickets spent $90

Marrrta [24]

Answer:

0 ≤ x ≤ 18

Step-by-step explanation:

Let 'x' be the number of youth tickets purchased at the zoo and 'y' be the number of adult tickets purchased at the zoo.

At a zoo, youth tickets cost $5 and adult tickets cost $9. A group spent a total of $90 on tickets. We can write as

5x + 9y = 90

to find x we divide both side by 5

x = (90-9y)/5 => 90/5 - 9y/5

x = 18 - 9y/5

The domain of the relationship is the possible set of values of x and y that satisfies the equation. The domain of this relationship is

0 ≤ x ≤ 18

At x = 0, it means only adult tickets were purchased.

At x = 18, it means only youth tickets were purchased.

4 0

3 years ago

The perimeter of a rectangular garden is 26 ft. What is the width of the

Morgarella [4.7K]

Answer:

21 is answer..........

8 0

3 years ago

Read 2 more answers

Please answer question

sweet-ann [11.9K]

Given;

ABCDE is similar to VWXYZ

so, the corresponding segments are proportional

We need to find the length of XY

XY is corresponding to CD

CD = 1.2 cm

Finding another two corresponding sides

DE = 3.2 cm , YZ = 4 cm

so,

$\begin{gathered} \frac{XY}{CD}=\frac{YZ}{DE} \\ \\ \frac{XY}{1.2}=\frac{4}{3.2} \\ \\ XY=\frac{4}{3.2}\cdot1.2=1.5\operatorname{cm} \end{gathered}$

So, the length of XY = 1.5 cm

3 0

1 year ago