John caught 24 trout in bass while on a fishing trip. The total weight of his catch was 137 pounds. The average weight of a trout was 2.5 pounds, and the average weight of a bass was 8 pounds. How many trout and how many bears did he catch?

trouts = 10 and bears = 14

Step-by-step explanation:

Let number of trouts and bears be x and y respectively.

This means that since he caught 24 trout and bass, we have;

x + y = 24 - - - (eq 1)

Now, average weight of trout is 2.5 pounds and average weight of bass is 8 pounds.

Thus;

2.5x + 8y = 137 - - - (eq 2)

From eq(1), let's make x the subject.

Thus;

x = 24 - y

Put 24 - y for x in eq(2)

2.5(24 - y) + 8y = 137

60 - 2.5y + 8y = 137

5.5y + 60 = 137

5.5y = 137 - 60

y = 77/5.5

y = 14

x = 24 - 14

x = 10

Thus, trouts = 10 and bears = 14

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step-by-step explanation:

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.