Minus' Solution to

Go Figure It Out Yourself!
Posted June 9 - 16, 1997

Minus decided to go with a little algebra this week to keep all of you on your toes...

Let S = Sarah's age
Let M = Mike's age

2S - 4 = S + 16
S = 20

M + 5 = 2M - 20
M = 25

Therefore, Mike is 5 years older than Sarah.

Taryn Chua, of Perth, Australia, really knew how to appeal to a fickle shark. She cooked up the perfect algebraic solution to this week's brain teaser.

I can form two equations:

s = Sarah's age m = Mike's age

2s - 4 = s + 16 AND m + 5 = 2m - 20

So now I solve them (using algebra)
2s - 4 = s + 16
2 - s = 16 + 4
s = 20
Sarah is 20 years old

m + 5 = 2m - 20
5 + 20 = 2m - m
25 = m
Mike is 25 years old

Mike is older than Sarah by 5 years (and nosy guests should keep their noses to themselves!)

The nosy guest, with the help of her trusty calculator, soon worked out that with clues that she had been given she could work out both people's ages.

She started by taking a wild guess at Sarah's age. She took a nice round number, 20, and used her calculator to figure out the cryptic clues that her date had given her. She was lucky enough to get it right first time. Having gotten that right, she then decided to try to figure out Mike's age. Her first number, which was 19, turned out to be wrong. Not to be discouraged, she raised the number to 25, which then turned out to be right. She then confidently turned to tell her date that Mike was 5 years older than Sarah, but found that he was gone, out of sheer boredom!!

Well from the information given we wrote two equations for Sarah and Mike.

2s - 4 = s + 16
2s - s = 16 + 4
s = 20

m + 5 = 2m - 20
20 + 5 = 2m - m
25 = m

So Mike is 25 years old and Sarah is 20 years old, so Mike is not marrying an older woman which is good because as we know women are the more mature gender so a younger male would be too immature for any normal female!!!

Sarah : 2x - 4 = x + 16
Mike : x + 5 = 2x - 20
Mike is obviously over 10 yrs old, and his age must also be a multiple of 5. Therefore, we have a limited amount of choices. We can tell at first glance that 15 and 20 will not work. Take 20 first, the lowest possible age, and you will see that this does not work. Our next choice is 25, and this option does work:
25 + 5 = 30, 25 x 2 = 50, and 50 - 20 = 30. - so this is correct.

We now have Mike's age. We can tell that for Sarah, x can be no lower than 17. So we start at 17, and find we are 3 off our target. If we try 18, we are 2 off. 19 is 1 off. There is an obvious pattern here, and we can tell because of this descending pattern that the next number 20, will be 0 off our target, and will be the correct answer.
20 x 2 = 40, 40 - 4 = 36, and 20 + 16 = 36. - so this is correct.

Another, much simpler way of working this puzzle out is by taking for Sarah: the 4 and 16, in the 2nd and 4th/last numeric position (including x) and adding the 2 together. The answer is 20, the correct answer.

Similarly for Mike: When 5 and 20, the 2nd and 4th/last numeric position (including x) are added together, the answer is 25, the correct answer.

This method will work with this type of question because of the number placement and number pattern. Therefore, Mike is older than Sarah by 5 years.

Hey, Minus, try getting your teeth into this! Let the age of Mark be m and s the age of Sarah. Then:

m = 2s - 4 = s + 16
m + 5 = 2m - 20
m = 25
Now we know what Mark's age is i.e. 25

2s - 4 = s + 16
2s = s + 20
s = 20
Sarah's age turns out to be 20.

Therefore it is true that Mark is older than Sarah by 5 years of age. That nosy woman can keep her thoughts to herself!

From, John(9 years of age at Harvard Uni)

P.S Hey Minus, these are really cool. Should keep making more of these problems!

Before I begin, I would like to clarify whose age we are talking about here. The nosy guest asked about Mike's bride, Sarah. Then that dopey partner of hers started going on about some chick called Jane. Now who am I writing about here? This is a conspiracy! I don't know how, but I am going to get you Minus, for wasting my time. You math sharks are nothing but trouble!

Your 25 year old Mike is obviously a sneaky husband with a confused friend and dating a 20 year old bird called Jane.

Given the clues in paragraph 2, we can set up the following algebra equations:

Let x = Sarah's age     Let y = Mike's age

2x - 4 = x + 16         y + 5 = 2y - 20
x - 4 = 16             -y + 5 = -20
x = 20 years old       -y = -25
                        y = 25 years old

Therefore, Mike is older by 5 years.

My solution is that Mike is older than Sarah by 5 years.
Take what the guest says(Twice Sarah's age, then minus 4 years to equal Sarah's age plus 16 years. Take Mike's age and add 5 years to equal twice Mike's age minus 20 years). Write it out using x as Sarah's age and y as Mike's. Now it says:

2x - 4 = x + 16
y + 5 = 2y - 20

Go through the equations, and it turns out that x = 20 and y = 25, therefore Sarah is 20 and Mike is 25, so Mike is 5 years older than Sarah.

Warren Yau [istr2859@fox.nstn.ca]
Matthew Armstrong [dennisa@pcug.org.au]
Lauren B. from St. Hilda's
Christian Tawfik [tawfik@merlin.fkp.univie.ac.at]
Tali Randall [trandall@hotmail.com]
Jesse McAlinden from St. Hilda's
Lin And Amy from St. Hilda's
Georgina Groves from St. Hilda's
Kylie Jack from St. Hilda's
Lib Devitt from St. Hilda's
The Pole Family [pole@comtek.com.au]
Susannah Kingsbury from St. Hilda's
Tanya Vahala St. Hilda's
Bec Johnson from St. Hilda's
Divya Nasta from St. Hilda's
Cindy Kua from St. Hilda's
Ivana Kuo from St. Hilda's
Felicity Pearce from St. Hilda's
Peter Mckerracher from Scotch College
Ben Dessauvagie from Scotch College