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 20 houses. Island A and Island C have a total of 13 houses. Island B and Island C have a total of 15 houses. A total of 24 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

Answer: A = 9

B = 11

C = 4

Explanation:

A + B = 20

A + C = 13

B + C = 15

A + B + C = 24

Substitute 20 into our final equation for A + B.

20 + C = 24. Subtract 20 from each side.

C = 4.

Remember, B + C = 15. Substitute 4 into C to solve for B.

B + 4 = 15. Subtract 4 from both sides.

B = 11

Remember, A + B = 20. Substitute 11 for B to solve for A.

A + 11 = 20. Subtract 11 from both sides.

A = 9.