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I am having trouble with a math problem and I'm hoping someone can help me figure it out. The problem goes as follows:

"There are twelve dogs in a kennel drinking water from a large water tank. How many liters of water do the dogs drink in total during an average day?

(1) The dogs drink an average of 3 liters of water per dog per day. (2) The four smallest dogs drink an average of 2 liters of water per dog per day and the four largest dogs drink twice as much on average. Each of the remaining dogs drinks on average the same amount as the overall average for all the dogs in the kennel."

I tried to solve the problem by first calculating the total water consumption of the smallest and largest dogs, and then adding the consumption of the remaining dogs. Here's my attempt:

Let x be the overall average water consumption per dog per day.

The four smallest dogs consume 2 liters of water per dog per day, so their total water consumption is 4 * 2 = 8 liters.

The four largest dogs consume twice as much on average, so their total water consumption is 4 * 2 * 2 = 16 liters.

The remaining 4 dogs consume on average the same as the overall average, which is x. So their total water consumption is 4 * x = 4x liters.

Adding all these up, we get the total water consumption:

8 + 16 + 4x = 24 + 4x liters

However, I'm not sure where to go from here to get the final answer. Can someone please help me out?

cricket900
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  • I suspect that the intent of the problem composer was for the problem solver to realize that all of the information in (2) above is redundant. How would you solve the problem, if the information in (2) above $~\color{red}{\text{was omitted?}}$ – user2661923 Mar 10 '23 at 00:43
  • As suggested by the answer of Ogglie Ostrich, since the information in (2) above implies that the information in (1) above is accurate, and since the information in (1) above is sufficient to solve the problem, the problem composer probably does not intend that (1) and (2) represent two different problems. – user2661923 Mar 10 '23 at 00:45
  • @user2661923 (1) and (2) are separate statements, and the task is to determine whether the problem can be solved with the statements separately, exclusively, or combined. – cricket900 Mar 10 '23 at 12:43

1 Answers1

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I'm a little unsure if $(1)$ and $(2)$ are seperate questions. As you will see, $(2) \implies (1)$, So I guess it doesn't matter regardless.

The 4 smallest dogs drink an average of 2 litres per day so together they drink an average of $4 \cdot 2 = 8$ litres per day. The 4 largest dogs drink an average of 4 litres per day, so together they drink an average of $4 \cdot 4 = 16$ litres per day. The remaining 4 dogs drink an average of $x$ litres per day, so together they drink an average of $4x$ litres per day, where $x$ is the average amount of water a dog in the kennel drinks.

The average each dog drinks is the average amount of water which is drunk each day: $8+16+4x$ divided by the number of dogs: $12$. We know that this is equal to $x$ so we have: $$\frac{24+4x}{12} = x \implies x=3$$ Then the average amount of total water the dogs drink per day is: $$24 + 4x = 36$$ If $(1)$ and $(2)$ are not separate questions, then $(1)$ tells you that $x=3$ explicitly, so you can just this into the expression you obtained for the total amount of water, $24+4x$, to get the correct answer.

Ogglie Ostrich
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  • (1) and (2) are separate statements, and the task is to determine whether the problem can be solved with the statements separately, exclusively, or combined. – cricket900 Mar 10 '23 at 12:43
  • Well as you can see above, its possible to solve the problem and get the same answer whether the statements are exclusive, separate or combined – Ogglie Ostrich Mar 11 '23 at 06:03