Digital PSAT Math Practice Question 274: Answer and Explanation

Question: 274

At a city park, there are three dogs that weigh an average of 40 pounds each, and three cats. If two of the cats weigh 25 pounds each, what must the weight (in pounds) of the third cat be if the average weight of all six of these animals in the park is 30 pounds?

Correct Answer: 10

Explanation:

10 The average of their weight would be the total weight of all six animals divided by 6:

where d_i represents the weight of dog i, and c_i represents the weight of cat i. You are told that the three dogs weigh an average of 40 pounds each, so and thus the three dogs combined weigh d₁ + d₂ + d₃ = 3(40) = 120. Also, you know two cats each weigh 25 pounds, so c₁ = 25 = c₂.

Thus, the average weight of the six animals is

You are told that the average weight is 30 pounds, and you want to find the weight of the third cat, so you set your above expression equal to 30 and solve for c₃:

First, multiply by 6:

170 + c₃ = 180. Next, subtract 170 from both sides:

c₃ = 10. Therefore, the cat of unknown weight weighs 10 pounds.