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Hailey is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Hailey will earn $\mathrm{}30$$30 every time one of her songs is played in a commercial and she will earn $\mathrm{}100$$100 every time one of her songs is played in a movie. Hailey’s songs were played on 4 times as many commercials as movies and her total earnings on the royalties from all commercials and movies was $440. Determine the number of commercials and the number of movies on which Hailey’s songs were played. Answer Ameryt iout of 2 See Answers Get the Answer.AI App Solve problem with AI Best Answer Let’s use the variables $c$c and $m$m to represent the number of times Hailey’s songs were played in commercials and movies, respectively. We know that Hailey earns $\mathrm{}30$$30 every time one of her songs is played in a commercial, so her total earnings from commercials would be $30c$30 c. Similarly, her total earnings from movies would be $100m$100 m.
We are told that Hailey’s songs were played on 4 times as many commercials as movies, so we can write:
$c=4m$c=4m
We are also told that Hailey’s total earnings on the royalties from all commercials and movies was $\mathrm{}440$\$440, so we can write:
$30c+100m=440$30 c+100 m=440
Now we can substitute $c=4m$c=4m into the second equation and solve for $m$m:
$\begin{array}{rl}30c+100m& =440\\ \\ 30\left(4m\right)+100m& =440\\ \\ 220m& =440\\ \\ m& =2\end{array}${:[30 c+100 m=440],[],[30(4m)+100 m=440],[],[220 m=440],[],[m=2]:}
So Hailey’s songs were played in 2 movies.
To find the number of commercials, we can use $c=4m$c=4m:
$c=4\left(2\right)=8$c=4(2)=8
So Hailey’s songs were played in 8 commercials.
Therefore, Hailey’s songs were played in 8 commercials and 2 movies.
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