Question

On a fishing trip, Mariko caught 24 fish. She caught some rockfish averaging 2.5lbs and some bluefish averaging 8lb. The total weight of the fish was 137lbs how may of each fish did she catch.

Answer 1

Mariko caught 10 rockfish and 14 bluefish on her fishing trip.

Step-by-step explanation:

Let's define the number of rockfish caught as x and the number of bluefish caught as y.

According to the given information, the average weight of each rockfish is 2.5lbs and the average weight of each bluefish is 8lbs.

We can form two equations based on the total weight of all the fish and the total number of fish caught:

1. Equation 1: x + y = 24 (since Mariko caught a total of 24 fish)
2. Equation 2: 2.5x + 8y = 137 (since the total weight of the fish was 137lbs)

We can solve this system of equations to find the values of x and y by either substitution or elimination method. Using the elimination method:

Multiplying Equation 1 by 2.5, we get 2.5x + 2.5y = 60

Subtracting this equation from Equation 2, we get 8y - 2.5y = 137 - 60

Simplifying, we have 5.5y = 77

Dividing both sides by 5.5, we get y = 14

Substituting this value back into Equation 1, we have x + 14 = 24

Simplifying, we get x = 10

Therefore, Mariko caught 10 rockfish and 14 bluefish.