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

Answer:

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

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

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;

$\begin{gathered} 3x+y=30\text{ -------1} \\ + \\ 5x-y=42\text{ ------------2} \\ = \\ 8x+0=72 \\ 8x=72 \\ x=\frac{72}{8} \\ x=9 \end{gathered}$

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;

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