Answer:
[tex]Third\ commerical\ takes\ 1 \frac{7}{30}\ minute.[/tex]
Step-by-step explanation:
Let us assume that the third commerical played time be x .
As given
Three commercials are played in a row between songs on the radio.
The three commercials fill exactly 3 minutes of time.
[tex]if\ the\ commercial\ uses\ 1 \frac{1}{6}\ minutes\ and\ the\ second\ uses\ \frac{3}{5}\ minute.[/tex]
i.e
[tex]if\ the\ commercial\ uses\ \frac{7}{6}\ minutes\ and\ the\ second\ uses\ \frac{3}{5}\ minute.[/tex]
Thus equation becomes
[tex]\frac{7}{6} + \frac{3}{5} + x = 3[/tex]
L.C.M of (6,5) = 30
[tex]\frac{7\times 5+ 3\times 6+30x}{30} = 3[/tex]
[tex]\frac{35+18+30x}{30} = 3[/tex]
35 + 18 + 30x = 3 × 30
35 + 18 + 30x = 90
30x= 90 -53
30x = 37
[tex]x = \frac{37}{30}\ minute[/tex]
Or
[tex]x =1 \frac{7}{30}[/tex]
[tex]Therefore\ third\ commerical\ takes\ 1 \frac{7}{30}\ minute.[/tex]
