The surface area of a spherical balloon measured in square inches is the same as its volume, measured in cubic inches.
What is the diameter of the balloon?
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Hint: The volume of a sphere is (4/3) * Pi * (r^3).
Answer: 6 inches.
The surface area of a sphere, of radius r, is 4 * Pi * (r ^ 2) and the volume is (4/3) * Pi * (r^3). Putting these equal and cancelling gives r = 3, which means the diameter is 6 inches.
At a recent visit to the reptile house at the local zoo, I counted a total of 27 heads and 70 feet.
I was counting snakes, lizards and people and I know that there were exactly twice as many lizards as people.
How many snakes did I count?
[Ref: ZLHO] © Kevin Stone
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Hint: Snakes don't have legs.
6 snakes: 7 people and 14 lizards.
If we have S snakes, L lizards and P people.
The 27 heads gives us:
S + L + P = 27 
The 70 feet gives us:
4L + 2P = 70 
We also know that:
L = 2P 
Using  in  gives:
4 x 2P + 2P = 70
10P = 70
P = 7
Using P = 7 in  gives:
4L + 14 = 70
4L = 56
L = 14
Using L = 14 and P = 7 in  gives:
S + 14 + 7 = 27
S = 6
So S = 6, P = 7 and L = 14.
Someone drove from Aardvark to Beeville.
On the first day they travelled 1/3 of the distance.
On day two they travelled 1/2 of the remaining distance.
On day three they travelled 2/3 of the remaining distance.
On day four, after covering 3/4 of the remaining distance, they were still 5 miles away from Beeville.
How many miles had they covered so far?
[Ref: ZNKP] © Kevin Stone
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Hint: Try working backwards.
The total trip was 180 miles. Working backwards:
Day 4: travelled 3/4 leaving 5 miles, which means that 5 miles is 1/4, so 20 miles were left at the start of Day 4.
Day 3: travelled 2/3 leaving 20 miles, which means that 20 miles is 1/3, so 60 miles were left at the start of Day 3.
Day 2: travelled 1/2 leaving 60 miles, which means that 60 miles is 1/2, so 120 miles were left at the start of Day 2.
Day 1: travelled 1/3 leaving 120 miles, which means that 120 miles is 2/3, so 180 miles were left at the start of Day 1.
Of the 180 miles overall, 175 were covered in the 4 days.
Can you Find a number...
...whose double exceeds its quarter by 7.
[Ref: ZHRW] © Kevin Stone
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Hint: The number is less than 100.
Whose double is 8 and quarter is 1.
If the missing number is N, then:
2N = N + 7
Multiply throughout by 4:
8N = N + 28
Subtract N from both sides:
7N = 28
Divide throughout by 7:
N = 4