Question

A car can travel 476 miles on 14 gallons of gas. Write an equation relating the distance d to the number of gallons g. How many gallons of gas does this car need to travel 578 miles?

Answer 1

d is directly proportional to g.

d α g

d = kg where k = constant, d =476, g =14

476 = k*14

476/14 = k

k = 34

d = kg

d = 34g is the equation.

When d = 578 miles, g = ?

578 = 34g

g = 578/34

g = 17

17 gallons would be needed.

Answer 2

Distance, d, is directly proportional to the number of gallons of gas, g. Thus,

d α g

To turn alpha to equal sign, we insert a constant of proportionality, k.

d=kg

To find k, we use the given conditions.
476 = k (14)
k = 34

Therefore, the equation is,
d = 34g

and for travelling 578 miles,
578 = 34g
g = 17 gallons is needed.