Question

Mr.Wilson's delivery truck used 12 5/8 gallons of gasoline in three days. If 5 1/3 gallons where used on the first day and 3 2/3 gallons were used on the second day, about how much gas is used on the third day?

Answer 1

Let's define

x: gas used on the third day

First, transform the mixed numbers into fractions, as follows:

`12(5)/(8)=(12\cdot8+5)/(8)=(101)/(8)`
`5(1)/(3)=(5\cdot3+1)/(3)=(16)/(3)`
`3(2)/(3)=(3\cdot3+2)/(3)=(11)/(3)`

The equation that relates these quantities is:

16/3 + 11/3 + x = 101/8

27/3 + x = 101/8

Solving for x:

`x=(101)/(8)-(27)/(3)=(101\cdot3-27\cdot8)/(8\cdot3)=(303-216)/(24)=(87)/(24)`

87/24 can be also expressed as follows:

`(87)/(24)=(3\cdot24+15)/(24)=(3\cdot24)/(24)+(15)/(24)=3(5)/(8)`

3 5/8 gallons of gas were used on the third day