After gemstones were fairly divided,
Grumpy's share was 1 diamond and 6 emeralds.
How many emerards equal in value to one diamond?
2007-11-26 06:08:36 · 4 answers · asked by Alexander 6 in Science & Mathematics ➔ Mathematics
3 emeralds equal 1 diamond.
D+6E = 1/7(16d + 15E)
7D+42E=16D+15E
27E=9D
3E=D
2007-11-26 06:11:41 · answer #1 · answered by Anonymous · 2⤊ 0⤋
Let D be the value of diamonds,
Let E be the value of emeralds.
The value of all the gems would be:
16D + 15E
The value of Grumpy's share of the total would be:
1D + 6E
And the total would be 7 times this:
7(1D + 6E)
Now equate these two:
16D + 15E = 7(1D + 6E)
Distribute the 7 through the parentheses:
16D + 15E = 7D + 42E
Group like terms together:
16D - 7D = 42E - 15E
9D = 27E
Divide both sides by 9:
D = 3E
Therefore:
1 diamond is equivalent in value to 3 emeralds.
As a double check figure everything in terms of the value of emeralds:
16 diamonds = 48 emeralds. So the total "stash" would be equivalent to 63 emeralds. Grumpy's share should be equivalent to 63/7 or 9 emeralds. Given that 1 diamond is equivalent to 3 emeralds, Grumpy did indeed get 1/7 of the gems.
Answer: 3 emeralds are equal in value to one diamond.
2007-11-26 14:12:22 · answer #2 · answered by Puzzling 7 · 2⤊ 0⤋
16d+15e=7n
1d+6e=n, 7d+42e=7n
subtract
9d-27e=0, 9d=27e, d=3e.
2007-11-26 14:14:12 · answer #3 · answered by JP 3 · 1⤊ 0⤋
***** grumpy he's an azzhole for not going equal with the rest of them
2007-11-26 14:11:27 · answer #4 · answered by Anonymous · 1⤊ 5⤋