application of solving system of equations

Question

200 tickets were sold in a school's annual musical performance. students' tickets cost $2.50 each and parents' tickets cost $3.50 each. the total amount collected was $537. how many tickets were sold for parents?

Answer 1

Let the number of student tickets sold be equal to X and let the number of parent tickets sold be equal to Y.

We know the total number of tickets sold is 200, so X + Y = 200.

We also know the total amount collected was $537, so X*2.50 + Y*3.50 = 537

We can solve for X and Y because we have two equations and two unknowns.

X + Y = 200 and can be converted into X = 200 - Y. We substitute "200 - Y" into the 2nd equation for X and get:

(200 - Y) * 2.50 + Y*3.50 = 537.

This simplifies to: 500 - Y*2.50 + Y* 3.50 = 537 or Y = 537 - 500 = 37. We substitute Y = 37 into the original equation: X + Y = 200, X + 37 = 200 => X = 163.

163 student tickets were sold and 37 parent tickets were sold.

Answer 2

p represents the number of parents tickets

200 - p represents the number of student tickets

3.50p + 2.50(200 - p) = 537.00

Can you solve for p and answer?