Using Systems of Equations.
Please help!!! I'm not sure what steps to do, to work this problem.
#7) Five hundred tickets were sold for a school play, which generated $3560 in revenue. The prices of the tickets were $5 for children, $7 for students, and $10 for adults. There were 180 more student tickets sold than adult tickets. Let x be the number of children tickets sold, let y be the number of student tickets sold, and let z be number of adult tickets sold. Find the number of each type of ticket sold.
Write a 3 by 3 system of equations to solve the problem stated above. Do not solve the system.
Equation 1: ______
Equation 2: ______
Equation 3: ______
(Write variable terms on the left-hand side each equation in aphabetical order. Write nonnegative constants on the right-hand side of each equation. Example: 3x-2y+z=20).
x + y + z = 500
5 x + 7 y + 10 z = 3560
y - z = 180
I just "translated" each English sentence into "math"
1) x + y + z = 500
2) 5x + 7y + 10z = 3560
3) y - z = 180
Okay. I understand. Thank you very much...
To solve this problem using systems of equations, we need to set up equations based on the given information.
Let's write the equations step by step:
Step 1: Write an equation for the total number of tickets sold:
The total number of tickets sold is the sum of tickets sold for children, students, and adults. Given that the number of children tickets sold is represented by x, the number of student tickets sold is represented by y, and the number of adult tickets sold is represented by z, we have the first equation:
x + y + z = 500
Step 2: Write an equation for the total revenue generated:
To find the total revenue, we need to multiply the number of tickets sold by their respective prices and sum them up. The equation for the revenue can be written as:
5x + 7y + 10z = 3560
Step 3: Write an equation relating the number of student tickets with the number of adult tickets:
The problem states that 180 more student tickets were sold than adult tickets. We can write this relationship as:
y = z + 180
Therefore, the system of equations is:
Equation 1: x + y + z = 500
Equation 2: 5x + 7y + 10z = 3560
Equation 3: y = z + 180