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.