Question

13 a carpenter buys 40 identical pieces of wood. the total value of the wood is $300. the carpenter makes a mistake in his measuring, so he then buys eight extra pieces of wood. he works out that the total value of the wood is now $375. is he correct? explain your answer. if the carpenter is not correct, what mistake do you think he has made?

Explanation:

Step1: Find cost per wood piece

$\text{Cost per piece} = \frac{\$300}{40} = \$7.5$

Step2: Calculate correct total cost

$\text{Total pieces} = 40 + 8 = 48$
$\text{Correct total cost} = 48 \times \$7.5 = \$360$

Step3: Compare to carpenter's value

Carpenter claims $\$375$, which differs from $\$360$.

Answer:

1. The carpenter is not correct. The correct total value of the wood should be $\$360$, not $\$375$.
2. His mistake is likely miscalculating the cost per piece or the total number of pieces. He may have incorrectly calculated the value of the 8 extra pieces as $\$75$ (instead of the correct $\$60$), possibly by using a wrong cost per piece (e.g., $\$9.375$ per piece instead of $\$7.5$) or miscounting the total number of pieces.