To solve this problem, we will use proportions. Proportions are ratios (fractions) that are related to each other. We always set proportions equal to each other. This will allow us to compare the correct ratio of height and weight compared to the weight given in the problem.
First, we need to convert the height of the gorillas into either feet or inches so that all of the heights are in the same units. 1 foot = 12 inches. I will convert the heights to inches. King Kong's height would be 236 inches: 19 ft multiplied by 12 inches per foot = 228 inches. 228 in plus 8 in = 236 in. The typical gorilla's height would be 66 inches: 5 ft multiplied by 12 inches per foot = 60 in. 60 in plus 6 in = 66 in.
Second, we need to convert the King Kong's weight in tons into pounds (lbs). This will match up with the units provided for typical gorilla weight (Also in pounds). 1 ton = 2000 pounds. Therefore, King Kong's weight would be 76000 pounds: 38 tons multiplied by 2000 pounds per ton = 76000 lbs. Since the typical gorilla's weight is between 300 and 500 lbs, I will use 400 lbs in my calculations.
Now that all of the heights are in inches and weights are in pounds, we will set up the proportion. The most important rule about proportions is that like units stay together. For example, if I have pounds as the unit in the numerator, I must place all of my units in pounds as the top number in the fraction. If we choose inches to be in the denominator, all units in inches will be placed in the bottom number of the fraction.
To check if 38 tons is reasonable for King Kong, we set up the proportion as follows:
X lbs King Kong. = 400 lbs typical gorilla
236 in King Kong 66 in typical gorilla
There are many ways to solve for X. For this problem, we will cross multiply and divide.
Cross multiply: 236 times 400 = 94400
Divide: 94400 divided by 66 = 1430
This means that X = 1430 pounds. Another way to think about it is that if a typical gorilla weighs 400 lbs with 66 in height, King Kong should weigh 1430 lbs while standing 236 in tall. The 38 ton (76000 lbs) King Kong weighs WAY too much compared to the typical gorilla. In fact, King Kong weighs about 53 times more than what he should!
