Disney held a breakfast

Question

Disney held a breakfast for parents and their children to eat with Mickey Mouse. Adult tickets cost $17.95 and children tickets cost $12.95. Disney made $7,355 in ticket sales from a total of 500 people that attended. How many adults and how many children were at the breakfast?

Answer 1

Let's call adults=x and children y. So we have x+y=500 (which is the total number of people). We also know that the total ticket sales are $ 7,355 when we know that tickets for adults cost $17,95 and for children $12,95. We can rewrite this as 17.95x+12.95y=7,355.

So we have 2 equations:

x+y=500

17.95x+12.95y=7,355.

Next, we express one of the variables (x or y) in terms of the other. For example, x=500-y.

Once we do that, we go ahead and plug (500-y) instead of x in the second equation, as follows:

17.95(500-y)+12.95y=7,355

8,975-17.95y+12.95y=7,355

8,975-7,355=5y

y=324

Answer 2

If a=number of adults

and c=number of children,

then a + c = 500 people total

Now, to find work with the total prices and total cost, you can make the equation:

(17.95 x a) + (12.95 x c) = 7,355

You now have two equations and two variables. There are several ways to solve this, but one of the easiest is to rearrange the first equation so that everything equals a and then substituting that a into the second equation, as shown below.

a + c - c = 500 - c

a = 500 - c

then, (17.95 x a) + (12.95 x c) = 7355

Plug in for a: 500 - c

17.95 x (500-c) + (12.95c) = 7355

distribute 17.95 to the (500 - c)

17.95 x 500 - 17.95c + 12.95c = 7355

multiply 17.95 times 500, combine the c: -17.95c + 12.95c

8975 - 5c = 7355

subtract 8975 from both sides

8975 - 5c - 8975 = 7355 - 8975

divide by -5

-5c/-5 = -1620/-5

solve for c:

c = 324 people

Now you still need to find the number of adults, so plug c into the first equation and solve:

a + c = 500

a + 324 = 500

a = 500 - 324

a = 176 people

Answer 3

17.95A + 12,95C = 7355

A + C = 500

You can switch the second equation to A = 500 - C by subtracting C from both sides of the second equation.

Then use substitution by substituting (500 - C) into the first equation for A.

17.95 (500 - C) + 12.95C = 7355

Use distributive property and multiply 17.95 to both parts of the ( ).

8975 - 17.95C +12,95C = 7355

combine the C's

8975 - 5C = 7355

-8975 -8975

-5C = -1620 divide both sides by -5

C = 324

then substitute back into A + C = 500

A + 324 = 500

-324 -324

A = 176

So there were 176 adults and 324 children.

But to check the answer sub the answers back into the first equation

17.95 (176 + 12.95 (324) = 7355, which it does work.