Math CentralQuandaries & Queries


Question from Renee, a parent:

Darlene's dog weighed 5 times as much as Leah's dog. Together, the dogs
weighed 84 pounds. How much did each dog weigh?
Write an equation and solve

Hi Renee,

I am going to suggest two ways to solve this problem.

Method 1:

Suppose Darlene has 5 dogs, each of which weighs the same as Leah's dog. The total weight of the six dogs is 84 pounds. How much does Leah's dog weigh?

Solve the problem this way and then proceed.

Method 1 ignores the instruction to "Write an equation and solve" but I like method 1 better than the algebraic, method 2 technique.

Method 2:

Let $w$ be the weight of Leah's dog in pounds. What is the weight of Darlene's dog? What is the total weight of both dogs? You know this is 84 pounds. Solve for $w.$

The two methods are really the same, one uses a variable $s$ and the other just uses logic.


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