Question
Joe sent out 100 emails in 5 days. Each day he sent out 6 more than the day before. Seventy five percent of all emails sent on the first day were not sent to his director. How many emails did he send to his director on the first day?
Answers
GPT 3.5
Let D be the number of emails sent to the director on the first day.
He sent out D + 0.75 * D = 1.75 * D emails on the first day
The number of emails sent each day increased by 6 so the number of emails sent on the second day was 1.75 * D + 6
On the third day, he sent out 1.75 * D + 6 + 6 = 1.75 * D + 12 emails
On the fourth day, he sent out 1.75 * D + 12 + 6 = 1.75 * D + 18 emails
On the fifth day, he sent out 1.75 * D + 18 + 6 = 1.75 * D + 24 emails
The sum of the number of emails sent each day is 1.75 * D + 1.75 * D + 6 + 1.75 * D + 12 + 1.75 * D + 18 + 1.75 * D + 24 = 5 * 1.75 * D + 60 emails.
He sent out 100 emails in total so 5 * 1.75 * D + 60 = 100.
Therefore 5 * 1.75 * D = 100 - 60 = <<5*1.75=8.75>>8.75
Therefore D = 8.75 / (5 * 1.75) = <<8.75/(5*1.75)=1>>1. Answer: \boxed{1}.
He sent out D + 0.75 * D = 1.75 * D emails on the first day
The number of emails sent each day increased by 6 so the number of emails sent on the second day was 1.75 * D + 6
On the third day, he sent out 1.75 * D + 6 + 6 = 1.75 * D + 12 emails
On the fourth day, he sent out 1.75 * D + 12 + 6 = 1.75 * D + 18 emails
On the fifth day, he sent out 1.75 * D + 18 + 6 = 1.75 * D + 24 emails
The sum of the number of emails sent each day is 1.75 * D + 1.75 * D + 6 + 1.75 * D + 12 + 1.75 * D + 18 + 1.75 * D + 24 = 5 * 1.75 * D + 60 emails.
He sent out 100 emails in total so 5 * 1.75 * D + 60 = 100.
Therefore 5 * 1.75 * D = 100 - 60 = <<5*1.75=8.75>>8.75
Therefore D = 8.75 / (5 * 1.75) = <<8.75/(5*1.75)=1>>1. Answer: \boxed{1}.