At the movie theatre, child admission is $5.70 and adult admission is $9.50, 146 tickets were sold for a total sales of $1075.40. How many adult tickets were sold that day?

x = number of children tickets sold = 82 tickets

y = number of adult tickets sold = 64 tickets

Step-by-step explanation:

Let

x = number of children tickets sold

y = number of adult tickets sold

x + y = 146 (1)

5.70x + 9.50y = 1075.40 (2)

From (1)

x = 146 - y

Substitute x = 146 - y into (2)

5.70x + 9.50y = 1075.40 (2)

5.70(146 - y) + 9.50y = 1075.40

832.2 - 5.70y + 9.50y = 1075.40

- 5.70y + 9.50y = 1075.40 - 832.2

3.8y = 243.2

y = 243.2/3.8

y = 64

Substitute y = 64 into (1)

x + y = 146

x + 64 = 146

x = 146 - 64

x = 82

x = number of children tickets sold = 82 tickets

y = number of adult tickets sold = 64 tickets

a

step-by-step explanation:

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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.