Question 9
a family has two cars. the first car has a fuel efficiency of 15 miles per gallon of gas and the second has a fuel efficiency of 25 miles per gallon of gas. during one particular week, the two cars went a combined total of 1350 miles, for a total gas consumption of 70 gallons. how many gallons were consumed by each of the two cars that week?

The first car consumed 40 gallons of gas and second car consumed 30 gallons of gas

Solution:

Let x = gallons consumed by car 1

Let y = gallons consumed by car 2

Fuel efficiency of car 1 = 15 miles per gallon

Distance covered in 1 gallon of gas = 15 miles

Fuel efficiency of car 2 = 25 miles per gallon

Distance covered in 1 gallon of gas = 25 miles

Given a total gas consumption of 70 gallons

Therefore,

gallons consumed by car 1  + gallons consumed by car 2 = 70

x + y = 70 ------ eqn 1

The two cars went a combined total of 1350 miles

Therefore,

gallons consumed by car 1  x distance covered in 1 gallon of gas of car 1 + gallons consumed by car 2 x distance covered in 1 gallon of gas of car 2 = 1350

15x + 25y = 1350 ----- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

x = 70 - y ------- eqn 3

Substitute eqn 3 in eqn 2

15(70 - y) + 25y = 1350

1050 - 15y + 25y = 1350

10y = 1350 - 1050

10y = 300

y = 30

Substitute y = 30 in eqn 3

x = 70 - 30

x = 40

Thus first car consumed 40 gallons of gas and second car consumed 30 gallons of gas

2(2x + 3) = -4 + 2(2x + 5)

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 6

4x - 6 + 6 = 4x - 6 + 6

4x = 4x

x = x

unlimited solutions.

let's first notice, the center of the hyperbola is at the origin, since the focus points are equidistantly 3 units away from the origin, that also means that the distance "c" from the center to either focus is 3.

it should also be notable that, the traverse axis for this hyperbola is vertical, or namely over the y-axis and therefore, the positive fraction will be the one with y-variable.

the traverse "a" component or distance from the center to either vertex is not 2, is more than 2, so we can safely put it at √5 ≈ 2.24.