How much would a 10th dog have to weight for the average weight in part (a) to be 250 pounds? Explain how you determined your answer.

Question

My dogs weghts are 6, 23, 20, 65, 55, 72, 53, 16, and 18.

Answer 1

The formula for average is the sum of the numbers divided by the number of numbers. In essence, we do not know what the 10th number is so we have x+the other numbers all over 10. The average needs to be 250.

250=(x+328)/10

Multiply both sides by 10. The equal sign means that anything you do to one side (except distribution) must be done to the other or they stop being equal.

2500=x+328.

Subtract 328 from both sides to get the weight of the missing dog. The dog will be x=2172 pounds. Luckily word problems seldom make logical sense.

Answer 2

The average weight of the 10 dogs will be given by:

Average weight = Total weight of the 10 dogs/10

Let the weight of the 10th dog be y pounds. Thus, the total weight of the 10 dogs is:

Total weight of 10 dogs = 6 + 23 + 20 + 65 + 55 + 72 + 53 + 16 + 18 + y = 328 + y

Therefore:

Average weight = (328 + y)/10

If the average weight for the dogs is 250 pounds, then:

250 = (328 + y)/10

Multiplying by 10 on both sides of the equation:

2,500 = 328 + y

Subtracting 328 from both sides of the equation, we have:

2,500 - 328 = 328 - 328 + y

y = 2,172

The weight of the 10th dog must be 2,172 pounds for the average weight of the 10 dogs to be 250 pounds.