SOLUTION: 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

Question 1202920: 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?

Found 4 solutions by josgarithmetic, greenestamps, MathTherapy, papachick24025:
Answer by josgarithmetic(39623)   (Show Source): You can put this solution on YOUR website!
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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.
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Taking off the work emails, of the emails were for friends+advertisements.

Taking off the email for friends, of were the 14 advertisements.

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Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

Fraction that were work related: 2/7

Fraction remaining: 1 - 2/7 = 5/7

Fraction that were from friends: 7/10 of the remaining = (7/10)(5/7) = 5/10 = 1/2

Fraction remaining: 1 - 2/7 - 1/2 = 14/14 - 4/14 - 7/14 = 3/14

Fraction that were advertisements: 3/4 of the remaining = (3/4)(3/14) = 9/56

He got 14 more emails from work than from advertisements:

(2/7)x - (9/56)x = 14
(16/56) - (9/56)x = 14
(7/56)x = 14
(1/8)x = 14
x = 14*8 = 112

ANSWER: 112

CHECK:
total: 112
work: (2/7)(112) = 32
other: 112-32 = 80
friends: (7/10)(80) = 56
other: 80-56 = 24
advertisements: (3/4)(24) = 18
work minus advertisements: 32-18 = 14

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

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 number of E-Mail messages he received be E Number of work-related E-Mail messages: Number of friends' E-Mail messages: Number of E-Mail messages for ads.: Since he received 14 more messages from work than from advertisements, we get: 16E = 9E + 14(56) --- Multiplying by LCD, 56 7E = 14(56) Number of E-Mail messages received, or

Answer by papachick24025(6)   (Show Source): You can put this solution on YOUR website!
In total, Eugene received 118 emails over the weekend.
Work emails = 2/7 of total emails
Friend emails = 7/10 of total emails (minus the work emails)
Advertising emails = 3/4 of total emails (minus the work and friend emails)
Work emails + Friend emails + Advertising emails = Total emails
2/7 + 7/10 + 3/4 = 1
Work emails = (14 + 3/4) / 1
Work emails = 17/4
Total emails = 17/4 + 7/10 + 3/4
Total emails = 112/10
Total emails = 112
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