Question

The crew on a boat catches 4 fish that weigh a total of 240 pounds. The king mackerel weighs twice as much as the blackfin tuna, and the wahoo weighs twice as much as the king mackerel. The weight of the sailfish is 5 times as much as the blackfin tuna. How much does each fish weigh?

a) Blackfin Tuna: 10 pounds, King Mackerel: 40 pounds, Wahoo: 80 pounds, Sailfish: 50 pounds
b) Blackfin Tuna: 10 pounds, King Mackerel: 20 pounds, Wahoo: 40 pounds, Sailfish: 200 pounds
c) Blackfin Tuna: 20 pounds, King Mackerel: 40 pounds, Wahoo: 80 pounds, Sailfish: 100 pounds
d) Blackfin Tuna: 20 pounds, King Mackerel: 40 pounds, Wahoo: 80 pounds, Sailfish: 400 pounds

Answer 1

By defining x as the weight of the blackfin tuna and setting up equations based on the given relationships between the weights of the fish, we find that option c) is correct: Blackfin Tuna weighs 20 pounds, King Mackerel 40 pounds, Wahoo 80 pounds, and Sailfish 100 pounds.

Step-by-step explanation:

We can solve this problem by setting up equations based on the information given. Let's let x represent the weight of the blackfin tuna. According to the information:

• • The king mackerel weighs twice as much as the blackfin tuna, so the king mackerel weighs 2x.
  • The wahoo weighs twice as much as the king mackerel, so the wahoo weighs 2(2x) = 4x.
  • The sailfish is 5 times as heavy as the blackfin tuna, so the sailfish weighs 5x.
  • The total weight of all four fish is 240 pounds.

So the equation to represent the total weight is:

x + 2x + 4x + 5x = 240

Combining like terms, we get:

12x = 240

Dividing both sides by 12 gives us:

x = 20

So the blackfin tuna weighs 20 pounds. Using this information, we can find out the weights of the other fish:

• • King Mackerel: 2x = 40 pounds
  • Wahoo: 4x = 80 pounds
  • Sailfish: 5x = 100 pounds

Therefore, option c) is correct: Blackfin Tuna: 20 pounds, King Mackerel: 40 pounds, Wahoo: 80 pounds, Sailfish: 100 pounds.