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Last month's solutions
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?
Answer: 582
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).