Solving for the Baby's Weight in a Complex Family Puzzle

Imagine a cheerful household consisting of a mother, a baby, and a dog, all weighing a combined 170 pounds. To add to the complexity, we know that the mother weighs 100 pounds more than the combined weight of the baby and dog, and that the dog weighs 60% less than the baby. What is the weight of the baby? This article explores the mathematical steps to uncover the answer.

Step-by-Step Calculation

We begin by defining the weights of the individuals in the household using variables:

M weight of the mother B weight of the baby D weight of the dog

The problem gives us three key pieces of information, which we can express as equations:

The total weight of the mother, baby, and dog together is 170 pounds: The mother weighs 100 pounds more than the combined weight of the baby and dog: The dog weighs 60% less than the baby:

Let's translate these into algebraic equations:

M B D 170 M B D 100 D 0.4B (since 60% less means 40% of the baby's weight)

Substituting and Simplifying

Next, we substitute the expression for D 0.4B into the first two equations.

M B 0.4B 170 which simplifies to M 1.4B 170 M B 0.4B 100 which simplifies to M 1.4B 100

We now have two expressions for M:

M 1.4B 100 M 1.4B 170

Solving the Equations

To solve for B, we substitute the first simplified expression for M into the second simplified equation:

1.4B 100 1.4B 170

Combining like terms, we get:

2.8B 100 170

Subtracting 100 from both sides:

2.8B 70

Dividing both sides by 2.8:

B 25

Verifying the Solution

Now that we have the baby's weight, we can find the weights of the dog and the mother:

D 0.4B 0.4 x 25 10 pounds M 1.4B 100 1.4 x 25 100 35 100 135 pounds

Let's verify the total weight:

M B D 135 25 10 170 pounds

Conclusion

The weight of the baby is 25 pounds.

Summary:

The baby weighs 25 pounds. The dog weighs 10 pounds. The mother weighs 135 pounds.

This complex puzzle reveals the interdependent relationships between the weights of a family, providing a fun and engaging way to practice algebraic problem-solving.