Answer
I asked for 7 feet, 4 inches and Alex brought me 4 feet, 7 inches.
Reasoning
If we label what I asked for as A feet and B inches, which is (12 x A + B) inches, then I actually received B feet and A inches, which is (12 x B + A) inches. Which means that:
5/8 x (12 x A + B) = (12 x B + A)
Simplifying gives:
A = 91/52 x B
As B is the number of inches, it can only be between 1 and 12 and must give A as a whole number of feet.
B = 4 is the only possible value, which means that A = 7.
So I originally asked for 7 feet, 4 inches.
Double-Checking
I received 4 feet, 7 inches = 55 inches.
I asked for 7 feet, 4 inches = 88 inches, and 88 x 5/8 = 55.
?
Puzzle 2
Below you can find a proverb.
The letters have been converted to their location in the alphabet.
Find two words, which are anagrams of each other, which complete this sentence:
Due to a recent outbreak of a ? infection in the zebra house, the local animal sanctuary had to ? their electron microscope correctly, to ensure rapid detection.
Hint
This is quite a tricky puzzle, and knowledge of algebra would certainly help.
Answer
The children tickets were £14, and the adult tickets were £18.
Reasoning
There are a number of methods for solving this problem, including:
Using a spreadsheet.Using a computer program.Using the intersection of lines on a graph.Using an online equation solver.Solving simultaneous equations using algebra.Solving simultaneous equations using inverse matrices.
Here is my solution using simultaneous equations and algebra.
First construct two algebraic equations, where 'c' is the number of children, and 'a' is the number of adults:
