Question

A baseball team is hosting a dance as a fundraiser. the cost of 1 individual ticket is $7. the cost of 1 group ticket is $16. the baseball team sold 36 more individual tickets than group tickets. the fundraiser raised $574 as a result of all ticket sales. if x is the number of the individual tickets that were sold and y is the number of group tickets that were sold, how many individual tickets were sold (what is the value of x)?

Answer 1

Word Problem

To form equations from word problems, we can do the following:

1. Identify variables
2. Find key information
3. Identify word equations and translate into numerical equations
4. Solve

Solving the Question

We're given:

• Let x be the number of individual tickets that were sold
• Let y be the number of group tickets sold
• Cost of 1x = 7 dollars
• Cost of 1y = 16 dollars
• Baseball team: 36 more x than y
  ⇒ x = 36 + y
• Fundraiser raised 574 dollars in total
  ⇒ 7x + 16y = 574 dollars

Question: How many individual tickets were sold? (What is the value of x?)

Here are all the equations we have created:

• x = 36 + y
• 7x + 16y = 574

We can solve for the value of x using systems of equations.

First, isolate y in the first equation:

`x = 36 + y\\y=x-36`

Now, plug this into the second equation:

`7x + 16y = 574\\7x + 16(x-36)= 574\\7x+ 16x-586= 574\\23x=1150\\\\x=(1150)/(23)\\\\x=50`

Therefore, x is equal to 50.

Answer

50 individual tickets were sold.