You can solve this by using two equations, each with two unknowns, or variables.

The variables are the number of cardholders tickets (C), and the number of non-cardholders tickets (N).

There were 305 tickets sold, so the total of cardholders plus noncardholders is 305:

N + C = 305

Each cardholders ticket costs 1.25, so the amount from sales of cardholders tickets is 1.25 * C.

Each non-cardholders ticket costs 2.50, so the amount from sales of non-cardholders tickets is 2.50 * N.

The total sales is 578.75:

1.25C + 2.5N = 578.75

You now have two equations in two unknowns. Now, change the first equation to express one of the variables in term of the other (by subtracting C from both sides of the equation:

N + C = 305

N = 305 - C

Now, use substitution to eliminate N from the second equation:

1.25C + 2.5N = 578.75

substitute for N:

1.25C + 2.5(305 - C) = 578.75

distributive property:

1.25C + (2.5 * 305 - 2.5 * C) = 578.75

perform multiplication inside the parentheses

1.25C + (762.5 - 2.5C) = 578.75

eliminate the parentheses

1.25C - 2.5C + 762.5 = 578.75

combine variable terms

-1.25C + 762.5 = 578.75

subtract 762.5 from both sides of the equation

-1.25C = -183.75

divide both sides by -1.25

C = 147

Now that you know how many cardholder tickets were sold, use the original equation to determine the non-cardholder tickets:

N + C = 305

substitute for C:

N + 147= 305

subtract 147 from both sides of the equation:

N = 305 - 147

N = 158

C = 147, N = 158

There were 147 cardholder tickets sold, and 158 non-cardholder tickets sold. Double check by plugging those values into the second equation:

1.25C + 2.5N = 578.75

1.25 * 147 + 2.5 * 158 = 578.75

183.75 + 395 = 578.75

578.75 = 578.75

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