### 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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