lheiannie07 wrote:A tiara is studded with a mixture of gems. The ratio of sapphires to emeralds is 3:1. If 6 emeralds are added, the tiara will contain an equal number of sapphires and emeralds. How many emeralds must be added to the original tiara so that the ratio between emeralds and sapphires is 3:1?
(A) 9
(B) 12
(C) 18
(D) 24
(E) 27
The ratio of sapphires to emeralds is 3:1.
Options for S and E:
S=3, E=1
S=6, E=2
S=9, E=3
S=12, E=4.
If 6 emeralds are added, the tiara will contain an equal number of sapphires and emeralds.
Adding 6 to the value of E in each of the options above, we get:
S=3, E=1+6=7
S=6, E=2+6=8
S=9, E=3+6=9.
We can stop here.
The option in blue yields an equal number of sapphires and emeralds.
How many emeralds must be added to the original tiara so that the ratio between emeralds and sapphires is 3:1?
In the blue option, the original values are as follows:
S=9, E=3.
After some emeralds are added, the resulting number of emeralds must be 3 times the original number of sapphires:
3S = 3*9 = 27.
Since the value of E must increase from 3 to 27, the number of emeralds that must be added = 27-3 = 24.
The correct answer is
D.
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