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Each month, a new set of puzzles will be posted.  Come back next month for the solutions and a new set of puzzles, or subscribe to have them sent directly to you.

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## Puzzle One

The price of an item was increased by 25% and later decreased by 25%, which makes the price of the item \$375. What was the original price?

Solution:

Let p = the original price

Then, 1.25 x 0.75 x p = 375

p = £400

## Puzzle Two

If 3/4 is Peter’s salary is equal to 2/4 of Mary’s salary. What is Peter’s salary if Mary’s salary is £120,000?

Solution:

Let: Peter’s Salary = p

Then, ¾ x p = ½ x 120,000

p = 4/3 x 60,000 = £80,000

## Puzzle Three

418 marbles are initially shared among three kids A, B and C. A got half the amount of C’s share which is 3 times B’s share. If A now wins 35 marbles from B and loses 8 marbles to B in a game of marbles how many marbles do each now have?

Answer: A ends up with 141 marbles, B ends up with 84 marbles, and C has 193 marbles

Solution:

Let x = C’s share

Givens:

A’s share = 1/2 of C’s share, so A’s share = x/2
C’s share = x = 3 x B’s share, so B’s share = x/3
418 = A + B + C = x/2 + x/3 + x = (11/6)(x)

Therefore:

x = (418)(6/11) = (38)(6) = 228 (or C’s share)
B’s share = x/3 = 228/3 = 76 marbles
A’s share = x/2 = 228/2 = 114 marbles
A + B + C = 114 + 76 + 228 = 418

If A now wins 35 marbles from C, but loses 8 marbles to B, then
A now has 114 + 35 – 8 = 141 marbles
B now has 76 + 8 = 84 marbles and
C now has 228 – 35 = 193 marbles

Checking answers, A + B + C = 141 + 84 + 193 = 418

## Puzzle Four

There is a three-digit number. The second digit is four times as big as the third digit (no zeros) while the first digit is three less than the second digit. What is the three-digit number?

Solution:

Let:

x = 1st single digit number
y = 2nd single digit number
z = 3rd single digit number
n = total 3-digit number where no two digits are the same or zero.

Given:
a) 100x + 10y + z = n
b) y = 4z
c) x = y – 3
d) z <= 3 (or 0, 1, 2, or 3)

z can = 1 or 2 but not = 0 or 3 because of step b) and y must be a single digit non zero.

If z = 1, then y = 4 from step b) and x = 1 from step c); x & z can not be the same value or 1)

Therefore, z = 2, then y = 8 from step b), x = 5 from step c) and n = 582 per step a).