Question

You are part of a construction company that is supposed to build houses. An architect has left plans to build houses on each island. Bridges connect the islands. Island A and island B have a total of 15 houses. Island A and island C have a total of 17 houses. Island B and island C have a total of 12 houses. A total of 22 houses is to be built on the three islands. Determine how many houses are to be built on each island. Explain how you arrived at your answer in detail.

Answer 1

Island A, B and C has 10, 5 and 7 houses respectively.

Explanation:

Let, the three islands A, B and C has a, b and c houses respectively.

According to the question, a + b = 15; a + c = 17; b + c = 12; a + b + c = 22.

Adding [ a + b = 15; a + c = 17]-these two, we get,
`a + (a + b + c) = 15 + 17 = 32\\a + 22 = 32\\a = 10`.

Now,
`a + b = 15\\10 + b = 15\\b = 5`.

`a + c = 17\\10 + c = 17\\c = 7`.