Brain Teasers
The Four-Stone Ring
While Christmas shopping, I chose a gold ring set with stones for my mother.
A ring set with 2 rubies and a diamond would have cost £3,000. One set with 4 amethysts and a diamond would come to £2,000. And 3 emeralds, 1 amethyst and a diamond would be £1,400.
Being a thoughtful son, I chose a ring that would have sentimental value. As my mother called her children Ellen, David, Richard and Andy, I have chosen a ring with one of each stone, to represent her children's names.
How much will my ring containing 1 emerald, 1 diamond, 1 ruby and 1 amethyst cost me?
A ring set with 2 rubies and a diamond would have cost £3,000. One set with 4 amethysts and a diamond would come to £2,000. And 3 emeralds, 1 amethyst and a diamond would be £1,400.
Being a thoughtful son, I chose a ring that would have sentimental value. As my mother called her children Ellen, David, Richard and Andy, I have chosen a ring with one of each stone, to represent her children's names.
How much will my ring containing 1 emerald, 1 diamond, 1 ruby and 1 amethyst cost me?
Hint
Finding the cost of each gem is not possible. It is still possible to find the value of the ring.Answer
The three rings can be expressed as:0E + 0A + 2R + 1D = £3,000
0E + 4A + 0R + 1D = £2,000
3E + 1A + 0R + 1D = £1,400
If we multiply the first line by 1.5 and divide the second line by 2, then total all three rings we get:
0E + 0A + 3R + 1.5D = £4,500
0E + 2A + 0R + .5D = £1,000
3E + 1A + 0R + 1D = £1,400
_________________________
3E + 3A + 3R + 3D = £6,900
£6,900 / 3 = £2,300
From this, we can see that a ring with one of each stone will cost me £2,300.
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