Three authors team up to write a childrens book. The publisher pays them according to the following contracts
Author - Fixed Rate - Royalty
Patricia $3000 - 1n
Stephan - $1500 - 2n
Harlan - $1000 - 3n
Find a simplified expression that represents the total that the publisher must pay the writing team
Determine the total payout if the book sells
* 200 copies
* 5000 copies
To find the total that the publisher must pay the writing team, we need to add up the payments for each author based on their respective contracts.
The payment for Patricia is a fixed rate of $3000. So, regardless of the number of copies sold, Patricia will receive the same amount.
The payment for Stephen is $1500 multiplied by 2n. This means that Stephen's payment depends on the number of copies sold, n. To simplify this expression, we can multiply $1500 by 2 to get $3000, and then multiply it by n. So, Stephen's payment can be expressed as 3000n.
The payment for Harlan is $1000 multiplied by 3n. Similar to Stephen, Harlan's payment also depends on the number of copies sold, n. To simplify this expression, we can multiply $1000 by 3 to get $3000, and then multiply it by n. So, Harlan's payment can be expressed as 3000n.
To find the total payout, we add up the payments for each author:
Total = Patricia's payment + Stephen's payment + Harlan's payment
Total = $3000 + 3000n + 3000n
Total = $3000 + 6000n
Now, let's calculate the total payout for different numbers of copies sold:
1. If the book sells 200 copies:
Total = $3000 + 6000(200)
Total = $3000 + 1200000
Total = $1203000
So, the total payout for 200 copies sold is $1,203,000.
2. If the book sells 5000 copies:
Total = $3000 + 6000(5000)
Total = $3000 + 30000000
Total = $30003000
So, the total payout for 5000 copies sold is $30,003,000.