please help me with math homework

Question

tickets of a program at college cost $5 for general admission or $4 with a student ID. If 181 people paid to see a performance and $797 was collected how many of each type of ticket were sold?

Answer 1

365 General Admission tickets

432 Student Admission tickets

Systems of Equations will work for this situation

Let x = non students

Let y = students

Equation 1 can represent the total number of people 181

x + y = 181

Equation 2 can represent the total cost $797

5x + 4y = 797

Equation 1 is ideal for setting up a substitution

x + y = 181

y = 181 - x

We will substitute this quantity for y in Equation 2

5x + 4y = 797

5x + 4(181 - x) = 797

5x + 724 -4x =797

Combine like terms

x + 724 = 797

Subtract 724 from both sides of the equation

x = 73

We can substitute our value for x in either equation to solve for y

x + y = 181

73 + y = 181

We already y = 181-x = 181- 73= 108

y = 108

We can use our values in both equations to check the values

73 + 108 = 181

5(73) + 4(108) = 797

365 + 432 = 797

Of course this can be done by elimination as another check. Give it a try.

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