I got this from http://www.purplemath.com/modules/systprob.htm, under the system-of-equation part:

* The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?

In the past I would have set this up by picking a variable for one of the groups (say, "c" for "children") and then use "(total) less (what I've already accounted for)" (in this case, "2200 – c") for the other group. Using a system of equations, however, allows me to use two different variables for the two different unknowns.

number of adults: a
number of children: c

total number: a + c = 2200
total income: 4a + 1.5c = 5050

Now I can solve the system for the number of adults and the number of children. I will solve the first equation for one of the variables, and then substitute the result into the other equation:

a = 2200 – c

4(2200 – c) + 1.5c = 5050
8800 – 4c + 1.5c = 5050
8800 – 2.5c = 5050
–2.5c = –3750
c = 1500

a = 2200 – (1500) = 700

There were 1500 children and 700 adults.

The part where I highlight it black is wrong isn't it? Because 4+1.5 is not 2.5, but it is 5.5, right? Or it is my mistake?


Thanks! :D

The problem I am seeing is that you are claiming that .5 of a child went to the fair

But that's not possible! How could 1/2 of a child went to the fair! They probably wrote the problem wrong?

That's -4+1.5, which is 2.5. Be careful of those signs.