154424

Diamonds= 96 pearls, Rubys= 24 pearls, Sapphires= 16 pearls, Pearl= Pearl.
Firstly I noticed that the one gift of 8 rubies , 10 sapphires, 100 pearls and 5 diamonds multiplied by the number of people gives an answer or product of 4. Subtracting this number 4 from the quantity of each gem gives you 4 rubies,6 sapphires, 96 pearls and 1 diamond. From this I gathered that any number divided by the remainders listed above leave you with remainders of relative or corresponding values. Essentially, If i divide the number 96 by all of the remainders individually, the values 24,16,96 and 1 and these are the values of the gems relative to the value of one pearl. Hence where I get the answer: Diamonds= 96 pearls, Rubys= 24 pearls, Sapphires= 16 pearls, Pearl= Pearl. I solved this through a similar method to substitution in algebra however my aim here was to find the value of one pearl relative to all the other gems. This was mainly because the quantity of pearls was the greatest and therefore it made sense to find the value of one pearl in relation to other as it was convenient and had the potential to be easily explained.