Mystery Unfolds

Spoke to my Dad recently, and while interviewing him about his siblings, he revealed something that never crossed my mind: our family name was not originally Banaag. His father, my grandfather Luis Banaag, was born Luis Banog. Apparently sometime after getting married, he decided to change his last name, for reasons we will probably never know.

I thought it was just a misspelled name. :)

Name	Luis Banog
Birth Date	1891
Age	38
Spouse's Name	Felipa Cadano
Spouse's Birth Date	1911
Spouse's Age	18
Event Date	10 Aug 1929
Event Place	San Juan, Batangas, Philippines
Father's Name	Gregorio Banog
Mother's Name	Levirma Magsono
Spouse's Father's Name	Eugenis Cadano
Spouse's Mother's Name	Pedra De Los Agueles

Citation

"Philippines Marriages, 1723-1957," database, FamilySearch (https://familysearch.org/pal:/MM9.1.1/FN8K-6P2 : 6 December 2014), Luis Banog and Felipa Cadano, 10 Aug 1929; citing San Juan, Batangas, Philippines, reference ; FHL microfilm 1,747,784.

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