Let's define
x: gas used on the third day
First, transform the mixed numbers into fractions, as follows:
[tex]12\frac{5}{8}=\frac{12\cdot8+5}{8}=\frac{101}{8}[/tex][tex]5\frac{1}{3}=\frac{5\cdot3+1}{3}=\frac{16}{3}[/tex][tex]3\frac{2}{3}=\frac{3\cdot3+2}{3}=\frac{11}{3}[/tex]The equation that relates these quantities is:
16/3 + 11/3 + x = 101/8
27/3 + x = 101/8
Solving for x:
[tex]x=\frac{101}{8}-\frac{27}{3}=\frac{101\cdot3-27\cdot8}{8\cdot3}=\frac{303-216}{24}=\frac{87}{24}[/tex]87/24 can be also expressed as follows:
[tex]\frac{87}{24}=\frac{3\cdot24+15}{24}=\frac{3\cdot24}{24}+\frac{15}{24}=3\frac{5}{8}[/tex]3 5/8 gallons of gas were used on the third day
