Question

at the city museum, child admission is $5.30 and adult admission is $8.80. On Wednesday, 154 tickets were sold for a total of $1,050.70. How many adult tickets were sold that day?

Answer 1

This problem can be solved using a system of equations. As in any word problem, the first thing we want to do is to turn our information into variables. So what information do we have?

We have child admission (c) and adult admission (a) as our relevant variables.

Now, what do we know?

The first thing we know is that 154 tickets were sold on Wednesday. So our number of child tickets plus our number of adult tickets is equal to 154.

a + c = 154.

This in itself isn't enough information. (A nice piece of knowledge; to solve for a system of n unsolved variables, we require a minimum of n equations to do so. So we need at least 2 equations for our 2 variables!)

Fortunately, we also know that the total amount of money brought in on Wednesday is equal to $1,050.70. We know child tickets cost $5.30, and adult tickets cost $8.80. How can we show this algebraically?

5.3c + 8.8a = $1,050.70

So now we have our system of equations. We know the number of adult + child tickets = 154, and the total costs of our tickets are $1,050.70.

a + c = 154.
5.3c + 8.8a = $1,050.70.

There are multiple ways to solve the system from here, but the simplest way I can see is to get rid of one of our equations entirely. The way we do this is by subtracting our entire first equation (a + c = 154) from the second equation.

But! We know that we need to remove at least one of our variables to do this. If we did it now, we'd have 4.3c + 7.8a = $900-something. This won't work. So first, we need to scale up the first equation, like so:

5.3a + 5.3c = 816.2
8.8a + 5.3c = 1,050.70

Now, we can subtract our entire first equation from both equations. So we have:

0a + 0c = 0
3.5a + 0c = 234.50

Removing all those unnecessary zeroes, we simply get:

3.5a = 234.50.

Now we simplify:

a = 67.

Our question is answered, but I'm going to continue on for educational purposes. Now we can just substitute "a" into either of our original equations to find c. The first one is easiest.

a + c = 154.
67 + c = 154.
c = 87.

So we now have our answer; a = 67, c = 87.

We sold a total of 67 adult tickets on Wednesday.

Answer 2

thank you

Answer 3

Any time. If you're not sure how exactly I performed one of the steps, feel free to ask and I'll try and clarify further.

Answer 4

wait so the answer would be 67 ???