Eugene received many emails over the weekend. 2/7 of the emails were work related and 7/10 of the remaining mails were from friends. 3/4 of the remaining emails were advertisements. Given that Eugene received 14 more emails from work than from advertisements, how many emails did he get over the weekend?
Let X be the total number of emails Eugene received.
After work-related emails, Eugene received X - 2/7*X = 5/7*X friend mails.
After friends, Eugene received 5/7*X - 7/10*5/7*X = 3/10*X ads.
Eugene received 14 more work-related emails than ads: 2/7*X - 3/10*X = 14.
Multiplying both sides by 70, we get 20X - 21X = 980.
Adding 21X to both sides, we get -980 = X.
Thus, Eugene received -980 emails over the weekend. Answer: \boxed{980}.
Let's solve this step-by-step:
Let's assume the total number of emails Eugene received over the weekend is x.
We know that 2/7 of the emails were work-related. Therefore, the number of work-related emails is (2/7) * x.
The remaining emails after work-related emails are x - (2/7) * x = (5/7) * x.
We also know that 7/10 of the remaining emails were from friends. Therefore, the number of friend emails is (7/10) * (5/7) * x = (35/70) * x = (1/2) * x.
The remaining emails after friend emails are (5/7) * x - (1/2) * x = (10/14) * x - (7/14) * x = (3/14) * x.
We are given that 3/4 of the remaining emails were advertisements. Therefore, the number of advertisement emails is (3/4) * (3/14) * x = (9/56) * x.
We are also given that Eugene received 14 more emails from work than from advertisements. This can be represented as (2/7) * x - (9/56) * x = 14.
Simplifying the equation:
(32/56) * x - (9/56) * x = 14,
(32 - 9)/56 * x = 14,
23/56 * x = 14,
x = (14 * 56)/23.
Calculating x:
x ≈ 32.17.
Therefore, Eugene received approximately 32.17 emails over the weekend.