Answer:
\(Third\ commerical\ takes\ 1 \frac{7}{30}\ minute.\)
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.
\(if\ the\ commercial\ uses\ 1 \frac{1}{6}\ minutes\ and\ the\ second\ uses\ \frac{3}{5}\ minute.\)
i.e
\(if\ the\ commercial\ uses\ \frac{7}{6}\ minutes\ and\ the\ second\ uses\ \frac{3}{5}\ minute.\)
Thus equation becomes
\(\frac{7}{6} + \frac{3}{5} + x = 3\)
L.C.M of (6,5) = 30
\(\frac{7\times 5+ 3\times 6+30x}{30} = 3\)
\(\frac{35+18+30x}{30} = 3\)
35 + 18 + 30x = 3 × 30
35 + 18 + 30x = 90
30x= 90 -53
30x = 37
\(x = \frac{37}{30}\ minute\)
Or
\(x =1 \frac{7}{30}\)
\(Therefore\ third\ commerical\ takes\ 1 \frac{7}{30}\ minute.\)
