The weight W of an aluminum flatboat varies directly with the length L of the boat. If a 13-foot boat weighs 221 pounds, then what is the weight of the 5-foot boat
The weight of a 5-foot boat is ____ pounds.
Cross multiply and solve for x.
13/221 = 5/x
85
To solve this problem, we need to use the concept of direct variation.
Direct variation means that when two variables, in this case, the weight and the length of the boat, are directly proportional to each other. Mathematically, it can be represented as W = kL, where W is the weight, L is the length, and k is the constant of variation.
Let's first find the value of the constant of variation (k).
We are given that when the length (L) is 13 feet, the weight (W) is 221 pounds. Plugging these values into the equation:
221 = k * 13.
Now, we can solve for k:
k = 221 / 13 = 17.
So the constant of variation is 17. This means that for every 1-foot increase in length, the weight increases by 17 pounds.
Now, we can find the weight of a 5-foot boat by plugging the length (L) into the equation:
W = k * L = 17 * 5 = 85 pounds.
Therefore, the weight of the 5-foot boat is 85 pounds.