Question

How many gallonswere consumed by each of the two cars that week?

Answer 1

Step-by-step explanation:

Let us denote by x the gallons for the first car and y the gallons for the second car.

Now, according to the problem, we have that the first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas and during one particular week, the two cars went a combined total of 1500 miles. Then, we get the following equation:

Equation 1:

20x + 30y = 1500

On the other hand, the problem says that there is a total gas consumption of 55 gallons. Then, we obtain the following equation:

Equation 2:

x + y = 55

From this last equation, we obtain the following equation:

Equation 3:

y = 55 - x

Now, replacing this equation in equation 1, we get:

`20x+30(55\text{ -x})=1500`

Applying the distributive property, get

`20x+1650\text{ -30x}=1500`

this is equivalent to:

`20x\text{ - 30x = 1500 - 1650}`

this is equivalent to:

`\text{ - 10 x = -150}`

or

`10\text{x = 150}`

solving for x, we obtain:

`x\text{ =}(150)/(10)=15`

now, replacing this value in equation 3, we get:

`y=55-x\text{ = 55-15 = 40 }`

we can conclude that the correct answer is:

Answer:

First car: 15 gallons.

Second car: 40 gallons.