Write a system of equations for each story problem Then solv

Write a system of equations for each story problem. Then, solve the system.

a. Delano schools were putting on the play Cinderella. In all, 510 people saw the opening show and $2970 was made. Adult tickets cost $7 each and children’s tickets cost $5 each. How many adults and how many children attended the show?

x = cost equation:
y = people equation:

Work solving system:

Solution

Let x and y be the number of adults and the children respectively. Then 7x + 5y = 2970...(1).and x +y = 510..(2) .

On multiplying both the sides of the 2nd equation by 5, we get 5x+5y = 2550...(3).

Now, on subtracting the 1st equation from the 3rd equation, we get 5x+5y - 7x -5y = 2970-2550 or, 2y = 420 so that y = 420/2 = 210. Then, on substituting y = 210 in the 2nd equation, we get x +210 = 510 so that x = 510-210 = 300.

Thus, 300 adults and 210 children saw the opening show of Cindrella.