Mathematical Puzzles 

Workings

Hint

Answer
All of them!

Workings

Hint
Vowels (AEIOU) and consonants are each worth a different number of miles.

Answer
2,200 miles.

Vowels (AEIOU) are worth 300 miles and consonants are worth 200 miles.

Double-Checking
Argentina has 4 vowels (AEIA = 4 x 300), and 5 consonants (RGNTN = 5 x 200), for a total of 1,200 + 1,000 = 1,200 miles.

Workings

Hint
A little bit of algebra might help.

Answers
Drew is 7 years old. Glen is 4 years old.
Answer #1
The first question involves Drew (D) and Alex (A).

Drew is currently one fifth of Alex's age, so:

(1)      A = D x 5

In 21 years, Alex will be twice their age, so:

(2) A + 21 = (D + 21) x 2

Using (1) in (2) gives:

  A + 21 = (D + 21) x 2

 5D + 21 = (D + 21) x 2

 5D + 21 = 2D + 42

      3D = 21

       D = 7

So Drew is 7 (and Alex is 35).

Answer #2
The second question involves Glen (G) and Billie (B).

Billie is exactly seven times the age of Glen:

(3)     B = G x 7

In 8 years, Billie will be three times the age of Glen, so:

(4) B + 8 = (G + 8) x 3

Using (3) in (4) gives:

  B + 8 = (G + 8) x 3

 7G + 8 = (G + 8) x 3

 7G + 8 = 3G + 24

     4G = 16

      G = 4

So Glen is 4 (and Billie is 28).

Workings

Hint
The answer is a whole number less than 10.

Answer
3.

Reasoning
We can multiply throughout by 12,
    X     X     X     X
    -  -  -  +  -  =  -
    X     2     4     12

to give:

   12 - 6X + 3X = X

        12 - 3X = X

             12 = 4X

              3 = X

As required.

Double-Checking
    3     3     3     3
    -  -  -  +  -  =  -
    3     2     4     12

    1 - 1.5 + 0.75 = 0.25

              0.25 = 0.25, which confirms that 3 is correct.