The Three Boxes Puzzle

 

The Three Boxes Puzzle

Question :

You have three boxes labeled A, B, and C. Each box contains a certain number of coins. The total number of coins in the three boxes is 21. Box A contains twice as many coins as Box B, and Box C contains three times as many coins as Box B.

Given this information, can you determine how many coins are in each box?

Solution:

Let's represent the number of coins in Box B as $𝑥$.

1. Box A contains twice as many coins as Box B: So, the number of coins in Box A is $2𝑥$.
2. Box C contains three times as many coins as Box B: So, the number of coins in Box C is $3𝑥$.

Now, we know that the total number of coins in the three boxes is 21:

$𝑥+2𝑥+3𝑥=21$

$6𝑥=21$

$𝑥=\frac{21}{6}$

$𝑥=3.5$

However, since the number of coins must be a whole number, $𝑥$ cannot be 3.5. So, let's consider $𝑥=3$.

• $\text{Number of coins in Box A}=2\times 3=6$
• $\text{Number of coins in Box B}=3$
• $\text{Number of coins in Box C}=3\times 3=9$

Verifying:

$6+3+9=18$

So, the total number of coins is indeed 21, as required.

Therefore, the number of coins in each box is:

• Box A: 6 coins
• Box B: 3 coins
• Box C: 9 coins