Question

Bob drove 200 miles using 9 gallons of gas. At this rate, how many gallons of gas would he need to drive 420 miles?

(a) 18 gallons
(b) 19 gallons
(c) 20 gallons
(d) 21 gallons

Answer 1

To determine how many gallons of gas are needed to drive 420 miles, a proportion is used based on the existing rate of 200 miles/9 gallons, resulting in approximately 19 gallons of gas required for the trip.

Step-by-step explanation:

To solve this problem we can set up a proportion since we know that Bob drove 200 miles using 9 gallons of gas. The student wants to find out how many gallons of gas would be needed to drive 420 miles. To do this, we use the rate that has been given (200 miles/9 gallons) to find out the rate for 420 miles.

Set up the proportion as follows:
200 miles / 9 gallons = 420 miles / x gallons

To find x, we cross-multiply and solve for x:
(200)(x) = (420)(9)

200x = 3780

Now we divide both sides by 200 to isolate x:
x = 3780 / 200

x = 18.9

Since we cannot have a fraction of a gallon when purchasing gas, we would round up to the nearest whole gallon, which means Bob would need approximately 19 gallons to drive 420 miles. Therefore, the correct answer is (b) 19 gallons.