Answer:
Three toothpicks balance one cube.
Explanation:
Let B, T and C stand for bean, toothpick and cube respectively.
If two cubes and one bean are balanced by eight toothpick, this means:
2C + B = 8T
If one cube is balanced by one bean and one toothpick, this means:
B + T = C. Therefore, we have two equations:
2C + B = 8T
B + T = C
Multiplying the second equation by 2, we have:
2B + 2T = 2C
Rearranging the resulting equation, we have:
-2C + 2B = -2T. Therefore, we have:
2C + B = 8T
-2C + 2B = -2T
Adding the last two equations, we have:
3B = 6T
Divide both sides by 3, we have:
B = 2T
Hence, two toothpicks balances one bean.
From the question, we are told
B + T = C
Substituting B = 2T, we have:
2T + T = C
3T = C.
Therefore, three toothpicks balance one cube.