tool. To write systems of equations, you will need a few new tools for your math toolbox. Let’s take a look at a typical question for this lesson.
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?
The first sentence will lead to one of the equations. Akil caught 20 trout and bass.
However, you have to understand that Akil caught 20 fish, some trout and some bass. If you misread the problem as 20 of each kind of fish, you would not find the correct answer here.
What are some possibilities if Akil caught 20 fish and there were some trout and some bass?
Think of four possibilities. Copy and complete the first four rows of the table into your
tool.
When you have written your four possibilities, click on the blanks in the table below to reveal the combinations the instructor picked.
| Number of Trout | Number of Bass | Process | Total Number of Fish |
| Interactive button. Assistance may be required. ____ 1 | Interactive button. Assistance may be required. ____ 19 | Interactive button. Assistance may be required. ____ 1 + 19 | Interactive button. Assistance may be required. ____ 20 |
| Interactive button. Assistance may be required. ____ 3 | Interactive button. Assistance may be required. ____ 17 | Interactive button. Assistance may be required. ____ 3 + 17 | Interactive button. Assistance may be required. ____ 20 |
| Interactive button. Assistance may be required. ____ 10 | Interactive button. Assistance may be required. ____ 10 | Interactive button. Assistance may be required. ____ 10 + 10 | Interactive button. Assistance may be required. ____ 20 |
| Interactive button. Assistance may be required. ____ 15 | Interactive button. Assistance may be required. ____ 5 | Interactive button. Assistance may be required. ____ 15 + 5 | Interactive button. Assistance may be required. ____ 20 |
Why are the four I chose correct? How do you know? Think about it and click the link below to reveal an answer.
Interactive popup. Assistance may be required.
The number of trout and the number of bass always add up to 20.
You want to find an equation from this data. It will involve variables. If you look at the question again, they used the letters t, number of trout, and b, number of bass.
| Number of Trout | Number of Bass | Process | Total Number of Fish |
| 1 | 19 | 1 + 19 | 20 |
| 3 | 17 | 3 + 17 | 20 |
| 10 | 10 | 10 + 10 | 20 |
| 15 | 5 | 15 + 5 | 20 |
| t | b | Interactive button. Assistance may be required. ____ t + b | Interactive button. Assistance may be required. ____ 20 |
What equation can you get from the last row of the table?
From the first four rows, we get these equations:
1 + 19 = 20
3 + 17 = 20
10 + 10 = 20
15 + 5 = 20
Follow the pattern of the numbers.
Click the link below to reveal the answer.
Interactive popup. Assistance may be required.
t + b = 20.
We have one equation! Sometimes that’s enough to find the correct answer. Here is the word problem with four answer choices.
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, number of trout, and b, 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 |
Which answer choices can you eliminate?
Interactive popup. Assistance may be required.
A, C, D