With 230 ants (1380 legs), 3 puppies (12 legs), and 1 teacher (2 legs).
If we call the number of puppies P, then there were (P + 20) children and 10 x (P + 20) ants, and a single teacher. If we now count the legs, we get:
Puppies:
P x 4 = 4P
Children:
(P + 20) x 2 = 2P + 40
Ants:
10 x (P + 20) x 6 = 60P + 1200
Teacher: 2
A total of 66P + 1242
Giving:
66P + 1242 = 1440
66P = 198
P = 3
So there were 3 puppies, hence 23 children.
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Puzzle 235
Last week I drove from Aardvark to Beeville.
On the first day, I travelled 1/3 of the starting distance.
On day two, I travelled 1/2 of the remaining distance.
On day three, I travelled 2/3 of the remaining distance.
At the end of day four, after travelling 3/4 of the remaining distance, I was still 5 miles away from Beeville.
The total distance was 180 miles, but as I still had 5 miles to go, the required answer is 175 miles.
Reasoning
Let's try working backwards.
Day 4: I travelled 3/4, which means that the other 1/4 was 5 miles, and 20 miles were left at the start of day four.
Day 3: I travelled 2/3, which means that the other 1/3 was 20 mile, and 60 miles were left at the start of day three.
Day 2: I travelled 1/2, which means that the other 1/2 was 60 miles, and 120 miles were left at the start of day two.
Day 1: I travelled 1/3, which means that the other 2/3 was 120 miles, and 180 miles were ahead at the start of day one.
The full distance was therefore 180 miles, but we were asked how many miles I had travelled so far, and as I still had 5 to go the answer is 175 miles.
Double-Checking
Start distance: 180 miles.
Day 1: I travelled 1/3 of the distance (60 miles), leaving 120 miles.
Day 2: I travelled 1/2 of the distance (60 miles), leaving 60 miles.
Day 3: I travelled 2/3 of the distance (40 miles), leaving 20 miles.
Day 4: I travelled 3/4 of the distance (15 miles), leaving 5 miles.
