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

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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) About Me  (Show Source):
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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, 5%2F7 of the emails were for friends+advertisements.

Taking off the email for friends, 3%2F10 of 5%2F7 were the 14 advertisements.


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Answer by greenestamps(13203) About Me  (Show Source):
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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) About Me  (Show Source):
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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: matrix%281%2C4%2C+%282%2F7%29E%2C+%22%2C%22%2C+or%2C+2E%2F7%29
                            matrix%281%2C5%2C+%22Remainder%3A%22%2C+%285%2F7%29E%2C+%22%2C%22%2C+or%2C+5E%2F7%29

Number of friends' E-Mail messages: matrix%281%2C4%2C+%287%2F10%29%285E%2F%287%29%29%2C+%22%2C%22%2C+or%2C+E%2F2%29
                        

Number of E-Mail messages for ads.: matrix%281%2C4%2C+%283%2F4%29%283E%2F%2814%29%29%2C+%22%2C%22%2C+or%2C+9E%2F56%29
                        
Since he received 14 more messages from work than from advertisements, we get: matrix%281%2C3%2C+2E%2F7%2C+%22=%22%2C+9E%2F56+%2B+14%29
                                                                               16E = 9E + 14(56) --- Multiplying by LCD, 56
                                                                                7E = 14(56)
                                         Number of E-Mail messages received, or

Answer by papachick24025(6) About Me  (Show Source):
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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