Question 1202920
<pre>
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(1,4, (2/7)E, ",", or, 2E/7)}}}
                            {{{matrix(1,5, "Remainder:", (5/7)E, ",", or, 5E/7)}}}

Number of friends' E-Mail messages: {{{matrix(1,4, (7/10)(5E/(7)), ",", or, E/2)}}}
                        {{{matrix(1,5, "Remainder:", (3/10)(5E/7), ",", or, 3E/14)}}}

Number of E-Mail messages for ads.: {{{matrix(1,4, (3/4)(3E/(14)), ",", or, 9E/56)}}}
                        {{{matrix(1,5, "Remainder:", (1/4)(3E/14), ",", or, 3E/56)}}}
Since he received 14 more messages from work than from advertisements, we get: {{{matrix(1,3, 2E/7, "=", 9E/56 + 14)}}}
                                                                               16E = 9E + 14(56) --- Multiplying by LCD, 56
                                                                                7E = 14(56)
                                         Number of E-Mail messages received, or {{{highlight_green(matrix(1,7, E, "=", 14(56)/7, "=", 14(8), "=", highlight(112)))}}}</pre>