What does the elaphant weigh on plant B

Question

The ratio of the weight of an object on planet A is the weight of the same object on planet B is 100 to 3. If an elaphant weighs 4200 pounds on planet A found the elephant's weight on plantet B

Answer 1

The main thing to understand about this problem is that anything that weighs 100 pounds on planet A will weigh 3 pounds on planet B instead.  As a result, something weighing 200 pounds on A would weigh 6 pounds on B for instance.  For a 300 pound object on planet A, 9 pounds on planet B.  (This is a similar concept to ingredient ratios in a recipe, where if you need 3 cups of flour for a loaf of a certain bread but you want two loaves, you would use 6 cups instead.)

This concept can be generalized with a simple equation.   It involves some algebra but ultimately makes the process easier if you are not working with nice easy numbers.

We want an equation that translates what was said in the problem into math.  Fractions and ratios are related concepts--a 1:2 ratio will produce an equation involving 1/2. Realize that mathematically, the problem states that

W_A/W_B =100/3  (equation A)

Therefore, if you want the weight on planet B based on planet A you can solve the above equation for W_B.  First multiply both sides by W_B.

W_A =100*W_B/3

Then you can multiply both sides by 3/100

W_A*3/100=W_B

Naturally, it doesn't matter which side is right or left, and order of multiplication does not matter as we learned in elementary, so the equation becomes

W_B=3*W_A/100

From there you can simply substitute the weight on planet A for the elephant and perform the arithmetic to get the final number.

W_B=3*4200/100=3*42=126

Therefore, the elephant weighs 126 pounds on planet B.

Had you wanted to get from the weight on planet B to the weight on planet A you would be able to go back to equation A and solve for W_A instead.