Puzzle 61
Alex's child Drew is exactly one fifth of Alex's age.
In 21 years, Alex will be exactly twice Drew's age.
Blake is exactly seven times the age of their child, Glen.
In 8 years, Blake will be three times the age of Glen.
How old are Drew and Glen now?
Puzzle Copyright © Kevin Stone
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Hint
A little bit of algebra might help.
Answer
Drew is 7 years old and Glen is 4 years old.
The first half of the 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).
The second half of the question involves Glen (J) and Blake (B).
Blake is exactly seven times the age of Glen:
(3) B = J x 7
In 8 years, Blake will be three times the age of Glen, so:
(4) B + 8 = (J + 8) x 3
Using (3) in (4) gives:
B + 8 = (J + 8) x 3
7J + 8 = (J + 8) x 3
7J + 8 = 3J + 24
4J = 16
J = 4
So Glen is 4 (and Blake is 28).
Puzzle 62
What value of X makes the following correct:
Puzzle Copyright © Kevin Stone
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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.
Puzzle 63
Daft Dave, our local DIY expert, is renovating the local hospital.
He has to number each of the rooms in the hospital with plastic numbers.
However, he has run out of the number 9.
How many 9's must Dave buy in order to number all 1,000 rooms?
Puzzle Copyright © Kevin Stone
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Hint
Don't forget the extra 9's in 90, 91, etc.
Answer
300.
Start with: 9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99 – which is 20 9's.
We then repeat this for 100, 200, 300, up to 900 – which is 200 9's.
But from 900 to 999 we have an extra 100 9's as each starts with a 9.
So the total is 300.
Puzzle 64
Two friends were driving from their home to Manchester, Alex drove the first 90 miles, and Blake took over for the remainder of the journey.
On the way back, Alex drove to begin with, and Blake took over for the last 100 miles.
Who drove the furthest?
Puzzle Copyright © Kevin Stone
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Hint
It doesn't matter how far it was to Manchester.
Answer
Blake.
Reasoning
If we call the total distance T, we know that:
on the way there Alex drove 90 miles, and Blake drove T - 90 miles.
on the way back Alex drove T - 100 miles, and Blake drove 100 miles.
So, in total:
Alex drove 90 + (T - 100) = T - 10.
Blake drove (T - 90) + 100 = T + 10.
So Blake drove 20 miles more than Alex.
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