Question

Chloe was in a fishing competition at Lake Poinsett. She caught some bass and some trout. Each bass weighed 3 pounds, and each trout weighed 1 pound. Chloe caught a total of 30 pounds of fish. She received 5 points in the competition for each bass, but since trout are low in Lake Poinsett, she lost 1 point for each trout. Chloe scored a total of 42 points. Write two equations from the given information and solve for the number of bass and trout, respectfully.

Answer 1

The number of bass caught is 9, while the number of trout caught is 3;

`\begin{gathered} x=9 \\ y=3 \end{gathered}`

Step-by-step explanation:

Given that each bass weighed 3 pounds, and each trout weighed 1 pound.

Let x represent the number of bass and y represent the number of trout.

If Chloe caught a total of 30 pounds of fish, we have;

`3x+y=30\text{ -------1}`

Also, She received 5 points in the competition for each bass, but since trout are low in Lake Poinsett, she lost 1 point for each trout.

If Chloe scored a total of 42 points, we have;

`5x-y=42\text{ ------------2}`

To solve;

Adding equations 1 and 2 together;

`\begin{gathered} 3x+y=30\text{ -------1} \\ + \\ 5x-y=42\text{ ------------2} \\ = \\ 8x+0=72 \\ 8x=72 \\ x=(72)/(8) \\ x=9 \end{gathered}`

Solving for y;

`\begin{gathered} 3x+y=30 \\ 3(9)+y=30 \\ 27+y=30 \\ y=30-27 \\ y=3 \end{gathered}`

Therefore, the number of bass caught is 9, while the number of trout caught is 3;

`\begin{gathered} x=9 \\ y=3 \end{gathered}`