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Sagot :
Yello paint: 1 1/5
Green paint: 1 1/6
Blue paint: 7/8
After using 3/4 of each paint color, we have
- Yellow:
[tex]\begin{gathered} 1+\frac{1}{5}-\frac{3}{4} \\ \frac{5}{5}+\frac{1}{5}-\frac{3}{4} \end{gathered}[/tex]The least common multiple of 5 and 4 is 20, then...
[tex]\begin{gathered} \frac{5\cdot4}{5\cdot4}+\frac{1\cdot4}{5\cdot4}-\frac{3\cdot5}{4\cdot5} \\ \frac{20}{20}+\frac{4}{20}-\frac{15}{20} \\ \frac{20+4-15}{20} \\ \frac{9}{20} \end{gathered}[/tex]So, for yellow paint, we will have 9/20 gallons
- Green:
[tex]\begin{gathered} 1+\frac{1}{6}-\frac{3}{4} \\ \frac{6}{6}+\frac{1}{6}-\frac{3}{4} \end{gathered}[/tex]The LCM of 6 and 4 is 12
[tex]\begin{gathered} \frac{6\cdot2}{6\cdot2}+\frac{1\cdot2}{6\cdot2}-\frac{3\cdot3}{4\cdot3} \\ \frac{12}{12}+\frac{2}{12}-\frac{9}{12} \\ \frac{12+2-9}{12} \\ \frac{5}{12} \end{gathered}[/tex]So, for green paint, we will have 5/12 gallons
- Blue:
[tex]\frac{7}{8}-\frac{3}{4}[/tex]LCM of 4 and 8 is 8
[tex]\begin{gathered} \frac{7}{8}-\frac{3\cdot2}{4\cdot2} \\ \frac{7}{8}-\frac{6}{8} \\ \frac{7-6}{8} \\ \frac{1}{8} \end{gathered}[/tex]So, for blue paint, we will have 1/8 gallons
Now, we add them upp in order to obtain our anwser:
[tex]\frac{9}{20}+\frac{5}{12}+\frac{1}{8}[/tex]The LCM of 8, 12 and 20 is 120
[tex]\begin{gathered} \frac{9\cdot6}{20\cdot6}+\frac{5\cdot10}{12\cdot10}+\frac{1\cdot15}{8\cdot15} \\ \frac{54}{120}+\frac{50}{120}+\frac{15}{120} \\ \frac{54+50+15}{120} \\ \frac{119}{120} \end{gathered}[/tex]In conclusion, he will have left 119/120 gallons of paint
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