Question

Two cubes and one bean are balanced by eight toothpicks. One cube is balanced by one bean and one toothpick. How many toothpicks will balance the cube?

Answer 1

Answer:

Three toothpicks balance one cube.

Step-by-step 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.