We got our answer, but it took a long time to make the tables and come up with an equation. You want to eventually write the equations without making the tables. Look at the problem again.
Akil caught 20 trout and bass while on a fishing trip. The total weight of his catch was 112 pounds. The average weight of a trout was 3.5 pounds, and the average weight of a bass was 7 pounds. Which system of equations can be used to find t, the number of trout, and b, the number of bass, that Akil caught?
| A | t = 20 + b 3.5t + 7b = 112 |
C | t + b = 112 3.5t + 7b = 20 |
| B | t + b = 20 3.5t + 7b = 112 |
D | t = 112 + b 3.5t + 7b = 20 |
We know the answer is B.
Akil caught 20 trout and bass while on a fishing trip.
This means the total number of trout and bass is 20. What does the word total mean in math? Click the link below for the answer.
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Add. So the equation is t + b = 20.
The total weight of his catch was 112 pounds. The average weight of a trout was 3.5 pounds, and the average weight of a bass was 7 pounds.
These sentences give the equation 3.5t + 7b = 112. Do you see the pattern? Trout are 3.5 pounds each which gives 3.5t. Bass are 7 pounds each which gives 7b. Again, the total weight is 112 pounds so add 3.5t and 7b to get 112.
So how many trout and bass were there.
In this resource, you don’t have to solve the system of equations you wrote, but can you tell from this table which combination of trout and bass is correct and why?
| Number of Trout | Number of Bass | Process Column | Total Weight (pounds) |
| 4 | 14 | 3.5(4) + 7(14) | 112 |
| 8 | 12 | 3.5(8) + 7(12) | 112 |
| 10 | 11 | 3.5(10) + 7(11) | 112 |
| 20 | 6 | 3.5(20) + 7(6) | 112 |
| t | b | 3.5(t) + 7(b) | 112 |
Write your answer using your notes, then click the link below for the answer.
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The correct answer is 8 trout and 12 bass because they weigh a total of 112 pounds AND add up to 20 fish.