Final answer:
The cost of 3 pounds of trout is $96, and the cost of 5 pounds of salmon is $42.
Step-by-step explanation:
The equation 3x + 5y = 210 represents the situation where the cost of 3 pounds of trout (x) plus the cost of 5 pounds of salmon (y) is equal to $210. To solve for the values of x and y, we can use the method of substitution or elimination. Let's use substitution:
Step 1: Solve the equation 3x + 5y = 210 for x in terms of y.
3x = 210 - 5y
x = (210 - 5y) / 3
Step 2: Substitute the value of x in the second equation, which states that the total cost is $210:
(210 - 5y) / 3 + 5y = 210.
Step 3: Simplify and solve for y:
210 - 5y + 15y = 630.
Step 4: Continuing to solve, we find that 10y = 420.
y = 420/10 = 42.
Step 5: Finally, substitute the value of y back into the equation for x and solve for x:
x = (210 - 5(42)) / 3.
x = 96.
Therefore, the cost of 3 pounds of trout is $96, and the cost of 5 pounds of salmon is $42.