Best representation of word problems?

Question

Tom is 8 years older than Jane. Five years ago Tom was 3 times as old as Jane. How old is Jane now?

1. does x represent Jane's age or Tom's age

2. does x+8 represent Jane's age or Tom's age

The sum of two consecutive odd integers equals 12. What are they?

Does 'x' represent the smaller or larger integer?

x+2 represents the smaller or larger integer?

The tens digit of a number is twice the ones digit. The sum of the digits in the number is 12. What is the number?

does 'x' represent the tens or ones digit?

does '2x' represent the tens or ones digit?

Answer 1

For word problems involving 2 measures, it usually helps to let x be the 2nd one being mentioned.

First problem: Let x = Jane (jane is being mentioned secondly in the

                                         problem)

                          x + 8 = Tom

                    Working equation: (x+8) - 5 = 3 (x - 5)

second Problem: Let x = first odd integer

                          x + 2 = 2nd odd integer

Third problem: Let x = ones digit (2nd one being mentioned)

                         2x = tens digit

                  Working equation: x + 2x = 12

Answer 2

PROBLEM 1:

Usually you make x equal the thing you are looking for.  In this case you are asked for Jane's age now, so I would let x equal Jane's age now.  Similarly x + 8 would be Tom's age now ("Tom is 8 years older than Jane")

1. Yes

2. Yes

"Five years ago Tom was 3 times as old as Jane. How old is Jane now?"

(x + 8) - 5 = 3(x - 5)

PROBLEM 2:

Usually you start with the smaller odd integer being x.  The next odd integer would be two bigger.

1. smaller

2. larger

x + x + 2 = 12

PROBLEM 3:

Take your pick here.  I'd let x be the ones digit and 2x be the tens digit.

1. ones

2. tens

x + 2x = 12