Sam's gas tank is 1/6 full. After he buys 11 gallons of gas, it is 2/3 full. How many gallons can Sam's gas tank hold?
fraction of tank filled ... 2/3 = 4/6 ... 4/6 - 1/6 = 3/6 = 1/2
half a tank is 11 gal
To solve this problem, we can first determine the increase in the gas tank's capacity after Sam buys 11 gallons of gas.
Let's say the gas tank can hold x gallons of gas. We are given that initially the gas tank is 1/6 full, which means it contains (1/6) * x gallons of gas. After Sam buys 11 gallons, the gas tank becomes 2/3 full, so it contains (2/3) * x gallons of gas.
We can set up an equation to represent this situation:
(2/3) * x - (1/6) * x = 11
Now let's solve for x:
Multiplying both sides of the equation by 6 to eliminate the denominators, we get:
2x - x/3 = 66
Multiplying both sides by 3 to get rid of the fraction, we have:
6x - x = 198
Combining like terms, we find:
5x = 198
Dividing both sides by 5, we get:
x = 198/5
Therefore, Sam's gas tank can hold 39.6 gallons of gas.