Three times as many children as adults attend a concert on Saturday. An adult's ticket cost $7 and a child's ticket cost $3. The theater collected a total of $6,000. How many people bought tickets?
375
375
To solve this problem, we can set up a system of equations using the given information.
Let's assume the number of adults attending the concert is 'x'. According to the problem, three times as many children attended the concert as adults, so we can say the number of children is 3x.
Now, let's calculate the total amount collected from adults:
The cost of an adult's ticket is $7, and if 'x' adults attended the concert, the total amount collected from adults would be 7 * x = 7x dollars.
Next, let's calculate the total amount collected from children:
The cost of a child's ticket is $3, and if there were 3x children attending the concert, the total amount collected from children would be 3 * 3x = 9x dollars.
According to the problem, the total amount collected is $6,000. So, we can write the equation:
7x + 9x = 6000
Combining like terms, we have:
16x = 6000
Now, we can solve for 'x' by dividing both sides of the equation by 16:
x = 6000 / 16 = 375
Therefore, the number of adults attending the concert is 375, and the number of children attending is three times this amount, which is 3 * 375 = 1125.
To find the total number of people who bought tickets, we can add the number of adults and children:
Total number of people = 375 + 1125 = 1500
Therefore, a total of 1500 people bought tickets for the concert.
number of adults ---- x
number of children -- 3x
7x + 3(3x) = 6000
solve for x