Hey guys if you could help me that would be great!
The questions says, there are eight rubies, ten emeralds, and a hundred pearls, which are in thy ear-ring, my beloved, were purchased by me for thee at an equal amount; and the sum of the prices of the three sort of gems was three less than half a hundred; tell me the price of each, auspicious woman.
Enter the price of one pearl ??? , the price of one emerald ???? , and the the price of one ruby ????
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It then says , The word "equal" means that eight rubies cost as much as ten emeralds or a hundred pearls. The prices that add to "three less than half a hundred" are the prices for one pearl, or one emerald, or one ruby. If you knew the price of a pearl you could easily figure out the price of a ruby or an emerald, just try some suitable numbers for the price of a pearl.
r = the price of one ruby
e = the price of one emerald
p = the price of one pearl
We know from the problem statement
8r = 10e =100p
r + e + p = (100/2) - 3 = 47
Start by re-arranging the first equation, to solve for two of the variables.
8r = 10e
e = (8/10)r
8r = 100p
p = (8/100)r
Substitue those values into the second equation and solve for r:
r + (8/10)r + (8/100)r = 47
r(1 + 8/10 + 8/100) = 47
r = 47/(47/25) = 25
from there, just plug the value of r into the two equations we already solved for:
e = (8/10)*25 = 20
p = (8/100)*25 = 2