Question

The gasoline gauge on a van initially read 1/3 full. When 10 gallons were added to the tank, the gauge read 3/4 full. How many more gallons are needed to fill the tank?
show work please:)

Answer 1

Let x = total number of gallons


"The gasoline gauge on a van initially read 1/3 full."----> the amount of gas in the tank at first is x/3 gallons


"When 10 gallons were added to the tank, the gauge read 3/4 full" ---> x/3 + 10 = 3x/4


Now solve that equation for x


x/3 + 10 = 3x/4

12*(x/3) + 12*10 = 12*(3x/4)

4x + 120 = 9x

120 = 9x - 4x

120 = 5x

120/5 = x

24 = x

x = 24


So there are 24 gallons total.


At first, there are x/3 = 24/3 = 8 gallons in the tank. You add 10 more to get 8+10 = 18 gallons (which is 3/4 of 24)


So you still need 24 - 18 = 6 gallons