A charity fair raised $6,000 by selling 500 lottery tickets. There were two types of lottery tickets: A tickets cost $10 each, and B tickets cost $60 each. How many tickets of each type were sold?

a + b = 500

10 a + 60 b = 6000 divide this by ten

a + b = 500
a + 6 b = 600
------------ subtract
-5 b = -100

b = 20
so a = 480

check
480*10 + 20 *60 = 4800 +1200 = 6000 sure enough

To solve this problem, let's use a system of equations.

Let's assume the number of type A tickets sold is "x" and the number of type B tickets sold is "y."

According to the given information, the total number of tickets sold is 500:
x + y = 500 -- (Equation 1)

The total amount of money raised is $6,000, which is the sum of the money raised from selling type A tickets and type B tickets:
10x + 60y = 6000 -- (Equation 2)

Now we have a system of equations to solve simultaneously.
Here are two methods to solve this system; you can choose the one you prefer:

Method 1: Substitution Method

1. Solve Equation 1 to express x in terms of y:
x = 500 - y

2. Substitute the value of x in Equation 2:
10(500 - y) + 60y = 6000

3. Simplify and solve for y:
5000 - 10y + 60y = 6000
50y = 1000
y = 20

4. Substitute the value of y back into Equation 1 to solve for x:
x + 20 = 500
x = 480

So, 480 type A tickets and 20 type B tickets were sold.

Method 2: Elimination Method

1. Multiply Equation 1 by 10 to eliminate x:
10x + 10y = 5000 -- (Equation 3)

2. Subtract Equation 3 from Equation 2 to eliminate x:
(10x + 60y) - (10x + 10y) = 6000 - 5000
50y = 1000
y = 20

3. Substitute the value of y back into Equation 1 to solve for x:
x + 20 = 500
x = 480

So, 480 type A tickets and 20 type B tickets were sold.

Therefore, 480 type A tickets and 20 type B tickets were sold at the charity fair.

Let's assume that the number of A tickets sold is 'x' and the number of B tickets sold is 'y'.

According to the problem, we know that the total number of tickets sold is 500.

So, we have the following equation: x + y = 500 (Equation 1)

We also know that the total amount collected from the sale of A tickets is equal to the total amount collected from the sale of B tickets, which is $6,000.

So, we have the following equation: 10x + 60y = 6000 (Equation 2)

To solve this system of equations, we can use the method of substitution or elimination.

Let's solve it using the method of substitution:

From Equation 1, we can express x in terms of y:
x = 500 - y

Substituting the value of x in Equation 2, we get:
10(500 - y) + 60y = 6000

Expanding and simplifying the equation, we have:
5000 - 10y + 60y = 6000
50y = 1000
y = 20

Substituting the value of y back into Equation 1, we get:
x + 20 = 500
x = 480

Therefore, 480 A tickets and 20 B tickets were sold.