Mindbogglers

The cat would reach the top on the 17th day.
At the end of the 16th day, the cat would be 64 feet up in the air.
The next day, he would reach the top.

There are 9! or 362,880 different batting orders.

The ratio is 2:1.
Since the measures of the angles of a triangle are in the ratio of 1:2:3, and since the sum of the angles is 180 degrees, the angles have measures of 30 degrees, 60 degrees, and 90 degrees.
In a 30-60-90 triangle, the hypotenuse is twice the shorter leg.

The sides of the triangle are 13, 14, and 15, making 14 the base, the height 12, and the area 84.

The four numbers are 8, 12, 5, and 20.
8 + 2 = 10, 12 - 2 = 10, 5 x 2 = 10, and 20 / 2 = 10.
The sum of 8 + 12 + 5 + 20 = 45.

To solve, use four variables:
Let x = 1st number
let y = 2nd number
let w = 3rd number
let v = 4th number.

Then x + y + w + v = 45
and x + 2 = y -2 = 2w = v/2

In the second equation, solve for y, w, and v in terms of x:
y = x + 4
w = (x + 2)/2
v = 2x + 4.
Then substitute those values in equation one:
x + (x +4) + ((x+2)/2) + (2x+4) = 45
9x = 72. so x = 8.

The number is 88.

Ann is 18 years old.

Mary Ann

24 18 <-- ages now

18 12 <-- ages before

She had $3 originally.

Let x = amount she had originally.
Then x + 2 = 5 (x - 2)
12 = 4x
x = 3

It is 6.75 miles to the top of the hill.

Let x = distance to the top.
Then 2x/3 is the time it took Mr. P to go to the top.
(distance x divided by rate of 3/2)
Also, 2x/9 is the time it took for him to go down the hill.
So, 2x/3 + 2x/9 = 6 (the total time for the trip).
Therefore, 8x/9 = 6, so 8x = 54 and x = 6.75.

The scores of the two games were:
Lambkins 12, Lobos 0
Lobos 28, Lambkins 18

Let x = points scored by the Lambkins in the first game.
Let y = points scored by the Lobos in the second game.
Let z = points scored by the Lambkins in the second game.

z + x + y = 58
z = 1.5 x
y - z = 10

Solving simultaneously, x = 12, y = 28, z = 18

99 games.
There is one winner, so there must be 99 losers, and hence, 99 games played.

12 + 11 = 123
The sum of the two numbers gives the last one or two digits, and the difference of the two numbers gives the first one or two digits.
Let a = first number and b = second.
There are two possibilities:
a + b = 3 and a - b = 12 or
a + b = 23 and a - b = 1

Solving the first set of possibilities, you get 2a = 15 and a = 7.5 which does not work.
Solving the second set, you get 2a = 24, so a = 12 and b = 11 which does work.

The four amounts were $3.16, $1.25, $1.20, and $1.50.

The boy's age is 10 years old and the sister's age is 4 years old.

Let x = boy's age now
let y = sister's age

--- BOY SISTER EQUATION

now x y x = 2.5 y

last year x - 1 y - 1 x - 1 = 3 (y - 1)

2 years ago x - 2 y - 2 x - 2 = 4 (y - 2)

3 years ago x - 3 y - 3 x - 3 = 7 (y - 3)

Use any two of the equations to solve or
graph the four lines -- they would all intersect at (10, 4).

Here are some possible answers:

Halves Quarters Dimes Nickels Pennies

--- --- --- 100 ---

--- --- 4 91 5

--- --- 8 82 10

--- --- 12 73 15

--- --- 16 64 20

--- --- 20 55 25

--- --- 24 46 30

--- --- 28 37 35

--- --- 32 28 40

1 --- 39 --- 60

2 --- 30 8 60

--- 10 --- 40 50

--- --- 40 10 50

4 1 20 --- 75

--- 4 16 40 40

and many more

Second Place.
If you pass the person in second, you take second place, and they become third.

1, 2, and 3.
1 + 2 + 3 = 6
1 x 2 x 3 = 6.

If the numbers do not have to be all positive, then you could use -1, 0, and 1 or -5, 0 and 5, etc.

Fill the 5-gallon jug, pour it into the 3-gallon jug until the 3 gallon is full, and leaving 2 gallons in the 5-gallon jug.
Now pour the 3-gallon jug out.
Pour the remaining 2 gallons from the 5 gallon into the empty 3-gallon jug.
Now fill the 5 gallon from the faucet.
You now have exactly 7 gallons.

His son.

Try to pronounce the sentence like these characters: u472bmt.

This is the only number that includes all the digits arranged in alphabetical order.

James had the better average for the first week (5/11 = .454 to 3/7 = .428).
James had the better average for the second week (6/9 = .667 to 9/14 = .642).
However, even though James had a better average for each week,
Jackson had the better overall average (12/21 = .571 to 11/20 = .550)!

Libby.

Five minutes.

7.5 Degrees.

The answer is not zero. The hour hand moves too; at 3.15, it will actually be a quarter of the way between 3 and 4 (because a quarter of an hour has gone by).
The number of degrees in the entire clock is 360 degrees.
The number of degrees between 3 and 4 will be a 12th of that: 360/ 12 = 30 degrees.
And the hour hand will have traveled one quarter of the way between that 30: 30/ 4 = 7.5 degrees.

There are 72 bees in the swarm.

Since you can't have 4.5 bees, the answer is 72 bees.

There were 15 bees.

The formula for the number of times a ball rebounds before reaching a corner is P + Q - 2.

The expression is:

Check it:

The measure of angle DEB = 30 degrees.

Draw segment BZ such that angle CBZ = 20 degrees.
Then draw segment DZ.

Click here for a proof

Ms. Pleacher teaches English, history, and French.

Ms. Shickle teaches English, mathematics, and history.

Ms. Muller teaches mathematics, geography, and French.

Travis is married to Tina.

Trip is married to Tracey.

Thomas is married to Tricia.

Tina must be married to Travis or else there would be two people who could walk to the railroad station!

Here is the new window:

You can see that it is half the area of the original window:

The original window has an area of 9 square feet and the altered window has an area of 9/2 square feet.

They walked a total of 24 miles.

Let x = distance walked on level ground one-way.
Let y= distanced walked up hill one-way.
Then set up an equation for the time that it took for the whole trip:

So, in six hours, they walked 12 miles out and 12 miles back, for a total of 24 miles.