Medium Puzzles 

Workings

Hint
The first word begins with the letter A.

Answers
-s-e-d = ascend -p-a-g = sprang -r-f-r = prefer -y-r-d = hybrid -r-f-e = trifle -a-b-n = carbon -a-e-a = camera -o-d-g = hotdog -s-f-l = useful -i-s-e = tissue

Workings

Hint
The answer isn't a whole number of years, and algebra might be required.

Answer
29 years 2 months.

Reasoning #1
This answer is taken directly from the original book.

The age of Mamma must have been 29 years 2 months; that of Papa, 35 years; and that of the child, Tommy, 5 years 10 months. Added together, these make seventy years. The father is six times the age of the son, and, after 23 years 4 months have elapsed, their united ages will amount to 140 years, and Tommy will be just half the age of his father.

Reasoning #2
Here's my answer, with a little algebra.

If we call Tommy T, Mamma M and Papa P we can see that:

"our three ages add up to exactly seventy years" gives us:

(1)   T + M + P = 70

"Just six times as old as you" gives us:

(2)   P = 6 x T

In an unknown number of years (Y) "Shall I ever be half as old as you" gives us:

(3)   P + Y = 2 x (T + Y)

and "our three ages will add up to exactly twice as much as today" gives us:

   (T + Y) + (M + Y) + (P + Y) = 140

which can be written as

(4)   T + M + P + 3Y = 140

We can see from (4) and (1) that

     3Y = 70

so

(5)   Y = 70 ÷ 3

Using (2) and (5) in (3) we have

            P + Y = 2 x (T + Y)

   6 x T + 70 ÷ 3 = 2 x (T + 70 ÷ 3)

            4 x T = 70 ÷ 3

(6)             T = 70 ÷ 12

We can now use (6) in (2) to see that:

   P = 6 x T

   P = 6 x 70 ÷ 12

   P = 70 ÷ 2

And using the values for T and P in (1) we have:

              T + M + P = 70

   70 ÷ 12 + M + 70 ÷ 2 = 70

Multiply throughout by 12 to give:

   70 + 12 x M + 420 = 840

              12 x M = 840 − 420 − 70

              12 x M = 350

                   M = 350 ÷ 12

So:

   Tommy = 70 ÷ 12   = 5.83333  = 5 years 10 months.
   Papa  = 70 ÷ 2    = 35       = 35 years.
   Mamma = 350 ÷ 12  = 29.1666  = 29 years 2 months.

Workings

Hint
The words are linked by their letters.

Answer
Approved.

The initial letters spell ORANGE and the last letters spell INDIGO.

Workings

Hint
Think of the pages from 1 to 9, and then 10 to 99.

Answers
There are 147 pages. The number 3 appears 35 times.
Answer #1
For pages 1 to 9, there are 9 pages, which is 9 digits.

For pages 10 to 99, there are 90 pages, which is 180 digits.

This is a total so far of 189, therefore we require another 333 − 189 = 144 digits, which is another 144 ÷ 3 = 48 pages.

Taking us to 9 + 90 + 48 = 147 pages in total.

Answer #2
From page 1 to 147 we have 15 pages that end in 3:

   3, 13, 23, …, 143

We also have the ten pages that start with 30:

   30, 31, 32, …, 39

Plus the ten pages that start with 130:

   130, 131, 132, …, 139

For a total of 15 + 10 + 10 = 35 number 3's.