the weight w of an aluminum flatboat varies directly with the L length of the boat. If a 8-ft boat weighs 120 pounds, then what is the weight of a 7 ft boat?
8/120 = 7/w
Cross multiply and solve for w.
In this problem, we are told that the weight (w) of an aluminum flatboat varies directly with its length (L). This means that as the length of the boat increases, its weight also increases proportionally.
To find the weight of the 7 ft boat, we need to use the information given about the 8 ft boat.
We are told that the 8 ft boat weighs 120 pounds. Let's assign variables to the weight (w) and length (L) of this boat. We have w = 120 and L = 8.
Since the weight and length are directly proportional, we can write a proportion using these values:
w1/L1 = w2/L2
where w1 and L1 are the weight and length of the first boat, and w2 and L2 are the weight and length of the second boat (which we want to find). Plugging in the values we have:
120/8 = w2/7
Now let's solve for w2, the weight of the 7 ft boat:
120 * 7 = 8 * w2
840 = 8w2
Divide both sides of the equation by 8:
840/8 = 8w2/8
105 = w2
Therefore, the weight of the 7 ft boat would be 105 pounds.