Linda would like to hire a clown to perform at her son's birthday party. Clown city charges $100 for incidentals plus $30 per hour for hiring a clown to perform. Party performers charges $120 for incidentals plus $25 per hour. How many hours would Linda need to plan on so that Party Performers is less expensive than Clown City?
solve
100 + 30t = 120 + 25t
120+25x<100+30x
20x<5x
x>4
Greater than 4 hours.
To compare the costs of hiring a clown from Clown City and Party Performers, we need to determine the point at which the cost from Party Performers becomes less expensive than Clown City.
Let's denote the number of hours Linda needs to plan on as "x."
For Clown City:
Total cost = incidentals + (hourly rate * number of hours)
Total cost = $100 + ($30 * x)
For Party Performers:
Total cost = incidentals + (hourly rate * number of hours)
Total cost = $120 + ($25 * x)
To find the point where Party Performers is less expensive than Clown City, we need to set up an equation and solve for "x."
$120 + ($25 * x) < $100 + ($30 * x)
Simplifying the equation, we get:
$120 - $100 < ($30 * x) - ($25 * x)
$20 < $5 * x
Dividing both sides of the equation by $5, we get:
4 < x
Based on the equation, Linda would need to plan on more than 4 hours for Party Performers to be less expensive than Clown City.