Question

, Assuming that the relationship between the miles driven and the amount of gasneeded is DIRECT VARITION, and that your car uses 1.6 gallons to go to Salt Lake from yourhome in Clinton (32 miles). Find the amount of gallons of gas that your car needs to go to LasVegas from your house, knowing that Salt Lake is 420 away from Vegas.Then, using the right numbers,distanceFirst, find the constant of variation,gasolinesolve the equationMy car needsgallons

Answer 1

Given:

Car uses 1.6 gallons to go 32 miles

Let's find the amount of gallons of gas the car needs to travel 420 miles.

Here, the relationship between the miles driven and the amount of gas needed is direct variation.

Since it is a direct variation, we have the variation equation when y varies directly with x:

y = kx

Where k is the constant of variation.

Hence, we have:

32 = 1.6k

Let's solve for k.

Divide both sides by 1.6:

`\begin{gathered} (32)/(1.6)=(1.6k)/(1.6) \\ \\ 20=k \\ \\ k=20 \end{gathered}`

The constant of variation is 20.

The equation that represents this situation is:

y = 20x

Therefore, to find the amount of gallons of gas needed if the car travels 420 miles, substitute 420 for y and solve for x.

420 = 20x

Divide both sides by 20:

`\begin{gathered} (420)/(20)=(20x)/(20) \\ \\ 21=x \\ \\ x=21 \end{gathered}`

Therefore, the car needs 21 gallons of gas