Constructing Equations and Formulea: age of man & son

[gm_b]

Struggling to construct the right equation to work out this......"A man is nine times as old as his son. In nine years time, he will be only three times as old as his son. How old are each now" :?:

 

[gm_b]

Re: Constructing Equations and Formulea

.....a difficult paper for me this one :!: Heres another on the same theme....." The sum of two consecutive numbersis 37. What are the two numbers :?:

 

[Aladdin]

Re: Constructing Equations and Formulea

.....a difficult paper for me this one :!: Heres another on the same theme....." The sum of two consecutive numbersis 37. What are the two numbers :?:

Let them be ; A and A+1
A+A+1=37
2A+1=37
2A=36
A=36/2=18
So 18 and the next number is 19 .

 

[Deleted member 4993]

Re: Constructing Equations and Formulea

Struggling to construct the right equation to work out this......"A man is nine times as old as his son. In nine years time, he will be only three times as old as his son. How old are each now" :?:

Please share with us your work, indicating exactly where you are stuck - so that we know where to begin to help you.

For assistance in translating (word ? equation), go to:

http://www.purplemath.com/modules/translat2.htm

 

[tkhunny]

Re: Constructing Equations and Formulea

.....a difficult paper for me this one :!: Heres another on the same theme....." The sum of two consecutive numbers is 37. What are the two numbers :?:

Nit Picking: This is a bad question. What kind of numbers? Real Numbers are DENSE. We can ALWAYS put another Real number between any two given Real numbers. There is no such thing as "two consecutive [Real] numbers".

Solution: Let's assume the questioner means "two consecutive integers".

WRITE DOWN clear an concise defintions. Aladdin has a good example, but not a great example.

Find two consecutive numbers.

No Good:

I don't know what the numbers are!! (followed by panic)

OK, but maybe missing some given information:

Let them be A and B

Good:

Let them be A and A+1

Better:

A = the Lesser number
A+1 = the Greater Number

Best, Most Complete:

It has been requested that we locate two consecutive "numbers". As it is not possible to solve such a problem (proof for Real Numbers provided on request), I'll have to assume that the problem means to ask for two consecutive "integers". Having said that...

A = The Lesser of the Two Consecutive Integers
A+1 = The Greater of the Two Consecutive Integers

I dare you to put something like that on an exam!

Proof, just in case someone asks.

Proof by contradiction...

1) Suppose we have two consecutive Real Numbers, a and b.
2) Without loss of generality, let's assume that b > a.
3) By definition of "consecutive", there are no Real Numbers between a and b, meaning that no Real Number, c, exists with the property a < c < b.
4) We'll need to note that the Real Numbers are closed under addition, multiplication, and division by other than zero (0).
5) Let's construct the number c = (a+b)/2
6) Since b > a, c = (a+b)/2 > (a+a)/2 = 2a/2 = a, so that c > a
7) Likewise, since b > a, c = (a+b)/2 < (b+b)/2 = 2b/2 = b, so that c < b
8) We have a < c < b and the proof is complete. There IS a Real number between a and b and the premise in 1) must be rejected.

I double-dog dare you to put THAT on an exam.

P.S. Sorry, i was bored.

 

[Aladdin]

Re: Constructing Equations and Formulea

.....a
!

Proof, just in case someone asks.

Proof by contradiction...

1) Suppose we have two consecutive Real Numbers, a and b.
2) Without loss of generality, let's assume that b > a.
3) By definition of "consecutive", there are no Real Numbers between a and b, meaning that no Real Number, c, exists with the property a < c < b.
4) We'll need to note that the Real Numbers are closed under addition, multiplication, and division by other than zero (0).
5) Let's construct the number c = (a+b)/2
6) Since b > a, c = (a+b)/2 > (a+a)/2 = 2a/2 = a, so that c > a
7) Likewise, since b > a, c = (a+b)/2 < (b+b)/2 = 2b/2 = b, so that c < b
8) We have a < c < b and the proof is complete. There IS a Real number between a and b and the premise in 1) must be rejected.

I double-dog dare you to put THAT on an exam.

P.S. Sorry, i was bored.

I'm studying sequence these days , thats why i thought of this answer.