Let's hope you'd never rely on getting your answer with one equation. Let's make sure the second equation is correct. 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 |
The second equation is going to come from sentences two and three.
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.
You're looking for the number of trout and the number of bass that would make 112 pounds. This won't be easy to find, but play with your calculator until you come up with 112 pounds.
Here are a few wrong guesses I made. Don't feel bad if you can't find any that work right away.
You are trying to get to 112 pounds of fish. A first guess of 5 trout at 3.5 pounds each and 10 bass at 7 pounds each was too low. You raised the number of bass to 12, but it was still too low, only 101.5 pounds. Then a third guess of 5 trout and 14 bass was too high. Can you find four combinations of trout and bass to make 112 pounds? Don't take more than 5 minutes searching. But try to find at least two.
Copy and complete the first four rows of the table using your notes as you find combinations that work.
Highlight below to see the four that you might have gotten. There are many others that you may have found.
On the last row, write t and b and try to find the process for a total weight of 112.
| Number of Trout | Number of Bass | Process Column | Total Weight (pounds) |
| Interactive button. Assistance may be required. ____ 4 | Interactive button. Assistance may be required. ____ 14 | Interactive button. Assistance may be required. ____ 3.5(4) + 7(14) | Interactive button. Assistance may be required. ____ 112 |
| Interactive button. Assistance may be required. ____ 8 | Interactive button. Assistance may be required. ____ 12 | Interactive button. Assistance may be required. ____ 3.5(8) + 7(12) | Interactive button. Assistance may be required. ____ 112 |
| Interactive button. Assistance may be required. ____ 10 | Interactive button. Assistance may be required. ____ 11 | Interactive button. Assistance may be required. ____ 3.5(10) + 7(11) | Interactive button. Assistance may be required. ____ 112 |
| Interactive button. Assistance may be required. ____ 20 | Interactive button. Assistance may be required. ____ 6 | Interactive button. Assistance may be required. ____ 3.5(20) + 7(6) | Interactive button. Assistance may be required. ____ 112 |
| t | b | Interactive button. Assistance may be required. ____ 3.5(t) + 7(b) | Interactive button. Assistance may be required. ____ 112 |
What equation did you get? Click the link below to reveal the answer.
Interactive popup. Assistance may be required.
3.5t + 7b = 112.
Review the problem, both equations match answer choice B.