Math -Brain Teaser

[Classik]

A girl is 6 years younger than her brother, and the product of their ages is 135. How old would they be in 4 years time, each?

 

[Willie T]

x-6+x=135
2x-6+6=135+6
2x=141
2x/2=141/2
x=70.5
The brother's age would be 70.5 then and the girl's would be 64.5

Add 4, if you really want to be mean to the poor old folks.

 

[Classik]

x-6+x=135
2x-6+6=135+6
2x=141
2x/2=141/2
x=70.5
The brother's age would be 70.5 then and the girl's would be 64.5

Add 4, if you really want to be mean to the poor old folks.

70.5 * 64.5 = 4547.25 >> 135

 

[Sparkey]

MY GUESS:

A girl is 6 years younger than her brother, and the product of their ages is 135.

Response limited to whole numbers only:

The girl is 9 years old; her brother is 15.
CHECK: 9 x 15 = 135​

In four years she would be 13. Her brother will be 19.
The product of their ages then (after 4 years have passed) is 247.

 

[Classik]

Mathematical methods. Show all working.

 

[jasonc]

Mathematical methods. Show all working.

Common core or non common core methods?

 

[Michael74]

19 and 13

 

[Michael74]

Mathematical methods. Show all working.

You can factor it as a polynomial:

x(x-6)=135

x²-6x=135

x²-6x-135=0

(x-15){x+9)

 

[WIP]

(X - 6)X=135 (product of their ages means we multiply them to equal 135.
X^2 - 6X = 135 (simplify)
X^2 - 6X - 135 = 0
(X + 9)(X - 15) = 0 (Factor it out. +9 – 15 = -6, +9 * -15 = -135)
X = -9 or X = 15 (solve for both. Since one can’t be -9, 15 is the correct solution)
One girl is 15 and the other is 9.

Prove it.
(15 - 6)*15 = 9*15 = 135

Michael was a bit quicker on the draw. I couldn't remember how to use factorials. Been about 30 years.

 

[Michael74]

Great minds think alike WIP.

 

[Classik]

Great attempts, but the answers actually aint those

 

[Michael74]

Our answers are better than the real answers. Reality is over rated anyway.

 

[Michael74]

Are you searching for the quadratic formula solution?

x= (6 ± √ 576)/2=15 or -9

You could also graph the equation, and note where the curve intercepts the x axis.

 

[Michael74]

Then just add 4.

 

[Classik]

Then just add 4.

 

[Not_Now.Soon]

In 4 years the sister who's younger will be 13, and the brother will be 19. Nice brain teaser.

 

[Not_Now.Soon]

The key element to the question is the product of their ages being 135. If I'm correct on the meaning of the word, product means multiplying. It would be sum if it was adding the ages together.

 

[WIP]

Great attempts, but the answers actually aint those

Geez. I forgot the rest of the problem.

In four years they will be 15+4=19 and 9+4=13.

I'm done now. My brain hurts.