QuestionCarson earns \$20 per commercial and \$120 per movie. If he had 5 more commercials than movies and earned \$380, find the counts.

Studdy Solution

STEP 1

Assumptions1. Carson earns $20 every time one of his songs is played in a commercial. He earns$ 120 every time one of his songs is played in a movie3. The number of commercials on which his songs were played is5 more than the number of movies4. His total earnings from all commercials and movies was $380

STEP 2

Let's denote the number of commercials as $C$ and the number of movies as $M$ . We can write the following two equations based on the problem1. $C = M +5$ (since the number of commercials is5 more than the number of movies)
2. $20C +120M =380$ (since his total earnings from all commercials and movies was $380)

STEP 3

We can substitute the first equation into the second equation to solve for $M$ .
$20(M +5) +120M =380$

STEP 4

Expand the left side of the equation.
$20M +100 +120M =380$

STEP 5

Combine like terms.
$140M +100 =380$

STEP 6

Subtract100 from both sides of the equation.
$140M =280$

STEP 7

Divide both sides of the equation by140 to solve for $M$ .
$M =280 /140$

STEP 8

Calculate the value of $M$ .
$M =2$

STEP 9

Now that we have the value for $M$ , we can substitute it into the first equation to solve for $C$ .
$C =2 +5$

STEP 10

Calculate the value of $C$ .
$C =7$ Carson's songs were played on7 commercials and2 movies.

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QuestionCarson earns \$20 per commercial and \$120 per movie. If he had 5 more commercials than movies and earned \$380, find the counts.

Studdy Solution

STEP 1

STEP 2

STEP 3

We can substitute the first equation into the second equation to solve for $M$ .
$20(M +5) +120M =380$

STEP 4

Expand the left side of the equation.
$20M +100 +120M =380$

STEP 5

Combine like terms.
$140M +100 =380$

STEP 6

Subtract100 from both sides of the equation.
$140M =280$

STEP 7

Divide both sides of the equation by140 to solve for $M$ .
$M =280 /140$

STEP 8

Calculate the value of $M$ .
$M =2$

STEP 9

Now that we have the value for $M$ , we can substitute it into the first equation to solve for $C$ .
$C =2 +5$

STEP 10

Calculate the value of $C$ .
$C =7$ Carson's songs were played on7 commercials and2 movies.

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QuestionCarson earns \$20 per commercial and \$120 per movie. If he had 5 more commercials than movies and earned \$380, find the counts.

Studdy Solution

STEP 1

STEP 2

STEP 3

We can substitute the first equation into the second equation to solve for MMM.20(M+5)+120M=38020(M +5) +120M =38020(M+5)+120M=380

STEP 4

Expand the left side of the equation.20M+100+120M=38020M +100 +120M =38020M+100+120M=380

STEP 5

Combine like terms.140M+100=380140M +100 =380140M+100=380

STEP 6

Subtract100 from both sides of the equation.140M=280140M =280140M=280

STEP 7

Divide both sides of the equation by140 to solve for MMM.M=280/140M =280 /140M=280/140

STEP 8

Calculate the value of MMM.M=2M =2M=2

STEP 9

Now that we have the value for MMM, we can substitute it into the first equation to solve for CCC.C=2+5C =2 +5C=2+5

STEP 10

Calculate the value of CCC.C=7C =7C=7Carson's songs were played on7 commercials and2 movies.

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We can substitute the first equation into the second equation to solve for $M$ .
$20(M +5) +120M =380$

Expand the left side of the equation.
$20M +100 +120M =380$

Combine like terms.
$140M +100 =380$

Subtract100 from both sides of the equation.
$140M =280$

Divide both sides of the equation by140 to solve for $M$ .
$M =280 /140$

Calculate the value of $M$ .
$M =2$

Now that we have the value for $M$ , we can substitute it into the first equation to solve for $C$ .
$C =2 +5$

Calculate the value of $C$ .
$C =7$ Carson's songs were played on7 commercials and2 movies.