Question

Define a variable, used the let statement, set up an equation, then solve. Lynn put 3 7/8 gallons of gas in her gas tank. If there are now 18 1/6 gallons in the tank, how many gallons did she start with?

Answer 1

Define a variable, used the let statement, set up an equation, then solve. Lynn put 3 7/8 gallons of gas in her gas tank. If there are now 18 1/6 gallons in the tank, how many gallons did she start with?​

Let

x -----> initial amount of gas in the tank

we have that'

x+3 7/8=18 1/6

step 1

Convert mxed numbers to an improper fraction

3 7/8=3+7/8=31/8

18 1/6=18+1/6=109/6

substitute

x+31/8=109/6

x=109/6-31/8

x=(4*109-3*31)/24

x=343/24 gal

step 2

Convert to mixed number

343/24=336/24+7/24=14+7/24=14 7/24 gal

therefore

the answer is

14 7/24 gallons