There was a total of 6,872 adults and children at a concert. There were 2,150 more adults than children. How many adults were there at the concert?
Understand the Problem
The question is asking for the number of adults at a concert based on the total number of adults and children combined, and the fact that there are 2,150 more adults than children. We will need to set up equations to find the solution.
Answer
The number of adults at the concert is $4511$.
Answer for screen readers
The number of adults at the concert is $4511$.
Steps to Solve
- Define Variables
Let $A$ represent the number of adults and $C$ represent the number of children.
- Set Up Equations
Based on the problem statement, we have the following equations:
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The total number of adults and children: $$ A + C = 6872 $$
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The number of adults is 2,150 more than the number of children: $$ A = C + 2150 $$
- Substitute and Solve
Substitute the second equation into the first equation: $$ (C + 2150) + C = 6872 $$
- Combine Like Terms
Combine the terms involving $C$: $$ 2C + 2150 = 6872 $$
- Isolate $C$
Subtract 2150 from both sides: $$ 2C = 6872 - 2150 $$
- Calculate the Value of $C$
Perform the subtraction: $$ 2C = 4722 $$
Divide both sides by 2: $$ C = 2361 $$
- Find the Value of $A$
Now substitute back to find $A$: $$ A = C + 2150 = 2361 + 2150 = 4511 $$
The number of adults at the concert is $4511$.
More Information
At the concert, there were more adults than children, and this is a common scenario in many public events. The difference of 2,150 in numbers indicates a specific demographic, which can be useful for event planning.
Tips
- Not defining the variables clearly, which can lead to confusion when setting up equations.
- Forgetting to substitute correctly when solving the equations, which can result in an incorrect answer.
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