Writing systems of linear equations

Question

On a fishing trip, Marisela caught 32 fish. She caught some rockfish averaging 2.5 pounds and some bluefish averaging 6 pounds. The total weight of the fish she caught was 129 pounds. Write a system of equations to model the relationship between the number of rockfish,r, and bluefish,b, Marisela caught. How many of each kind of fish did she catch?

Answer 1

Let r = the number of rockfish Marisela caught and b = the number of bluefish she caught.

The we have two equations and two unknowns:

r + b = 32 and

2.5 x r + 6.0 x b = 129 From the first equation b = 32 - r Substituting for b in the second equation yields:

2.5 x r + 6 x ( 32 - r ) = 129 or

2.5 x r + 192 - 6 x r = 129

-3.5 x r = -63

So r = 18 and b = 14 You can check to see that this works.