Question

2. The admission fee at a small fair is $1.50 for children and $4 for adults.

On a certain day, 220 people enter the fair and $505 is collected. How
many children attended the fair that day?

Answer 1

26 children

Explanation:

Step 1 Create a system of equations

Firstly, we know that it cost $1.50 for children and $4 for adults and we know that 505$ is the total amount collected

So if x = number of children and y = number of adults

Then 1.50x + 4x = 505

We also know that 220 total people entered which consists of adults and children.
Again, if x = number of children and y = number of adults

Then we can say that x + y = 220

So we now have the two equations

1.50x + 4y = 505 and x + y = 220

Step 2 Solve the equation

There are many methods you can use to solve this equation however I'd recommend the substitution method as we can easily solve for x or y in the equation x + y = 220 and isolate one of the variables, we can then easily substitute that into the other equation.

Isolating y

x + y = 220

==> subtract x from both sides

y = 220 - x

We now substitute y into the other equation and solve for x(# of children)

1.5x + 4y = 505

==> plug in y = 220 - x

1.5x + 4(220 - x) = 505

==> distribute 4

1.5x + 440 - 4x = 505

==> combine like terms

-2.5x + 440 = 505

==> subtract 440 from both sides

-2.5x = -65

==> divide both sides by -2.5

x = 26

So 26 children attended the fair that day.