Random Math Question

Sometimes, when there's no workload, you try to find something to do. Someone at the office forwarded an email asking to solve a word problem, so it got me going. The problem goes like:

'A man wanted to get into his work building, but he had forgotten his pin-code. However, he did remember five clues.
These are what those clues were:
The fifth number plus the third number equals 14.
The fourth number is one more than the second number. The first number is one less than twice the second number.
The second number plus the third number equals 10.
The sum of all five numbers is 30.
What were the five numbers and in what order?'

Wow. Equations. So I opened my trusty notepad, and start translating the word problem to equations.

e + c = 14 (1)
d = b + 1  (2)
a = 2b - 1 (3)
b + c = 10 (4)
a + b + c + d + e = 30 (5)

Looking at the equations above, the most common variable is b. So we try to express all of the equations in terms of b.

Using (1) and (4), we get (6)
b + c = 10 (4)
c = 10 - b (6)

e + c = 14 (1)
c = 14 - e

Since both are equal to c, we solve to get (7).
14 - e = 10 - b
14 - 10 = e - b
4 = e - b
e = b + 4 (7)

We now have all equations with a common variable, b. Let's solve for b.
Plug (2), (3), (6) and (7) into (5)
(2b - 1) + b + (10 - b) + (b + 1) + (b + 4) = 30
4b + 14 = 30
4b = 30 - 14
4b = 16
b = 4

Substituting b,
(3) a = 2(4) - 1 = 7
     b = 4
(6) c = 10 - 4 = 6
(2) d = 4 + 1 = 5
(7) e = 14 - 6 = 8

Check:
7 + 4 + 6 + 5 + 8 = 30

At Last! Welcome to the Internet World!

After a bit of a wait, we finally got internet at home!

My wife and I have been wanting to have our own internet connection for a long time. Being a full time housewife, she's tied at home doing what good housewives do, and most of all, taking good care of our beautiful baby. But doing the routine everyday, every week, even dedicated housewives need some R&R.

Since we don't have cable TV, daily soaps have been a bore. She's been asking me when we could get connected so one day, when some sales agents were going around our subdivision, we decided to ask. Did the standard, and later in the afternoon, we're installed! My wife can't hide her smile. I had to use it first though; she's doing the laundry at the moment. =P She can enjoy it later.

At least now we don't have to beg for a connection. Ugh.

Finding Banaag in History

For a while now, I have been looking around the internet for persons with last name Banaag that I can find. I would like to see if somehow they were related to me, in any way. I have made a family tree for my immediate relatives in the interest of finding relations with other Banaags out there.

Familia Banaag - My Family Tree
Ancestry

Banaag, Leovigildo - This one I contributed to Wikipedia based on articles available online.
was a Representative of 1st Legislative District of Agusan del Norte (11th, 12th, 13th Congress)

Banaag, Aquilino - was a Representative of 2nd Legislative District of Pangasinan (4th Philippine Legislature)

Chan Robles Virtual Law Library
BANAAG, AMADEO V.; San Carlos, Pangasinan; April 01, 1953; Roll No. 3907.
BANAAG, ARMANDO S.; Batangas, Batangas; January 25, 1955; Roll No. 9068.
BANAAG, AVELINO V.; Dagupan City; January 26, 1961; Roll No. 15688.
BANAAG, BENEDICTO A.; Liloan, Cebu; May 23, 2001; Roll No. 45455.
BANAAG, BENITO S.; October 15, 1923.
BANAAG, DENNIS B.; Cagayan de Oro City; June 01, 1987; Roll No. 34913.
BANAAG, EDGARDO M.; Española, Palawan; May 6, 2004; Roll No. 49602.
BANA-AG, EDUARDO C.; Cebu City; June 10, 1975; Roll No. 25968.
BANAAG, EUSEBIO B.; Siocon, Zamboanga del Norte; June 15, 1959; Roll No. 14159.
BANAAG, GABRIEL R.; December 24, 1938.
BANAAG, GERVACIO S.; Mangatarem, Pangasinan; April 11, 1956; Roll No. 10456.
BANAAG, GIL U.; Talisayan, Misamis Oriental; June 04, 1992; Roll No. 37946.
BANAAG, GRACIANO; December 31, 1925.
BANAAG, GREGORIO C.; December 16, 1940.
BANAAG, ISAAC P.; City of Ozamiz; February 02, 1951; Roll No. 2292.
BANAAG, JOSELITO V.; Manila; May 06, 1999; Roll No. 43673.
BANAAG, LEOVIGILDO B.; Butuan City; March 14, 1969; Roll No. 22545.
BANAAG, TOMAS; Catarman, Misamis Oriental; May 26, 1948; Roll No. 843.