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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)?

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theleangreenbean

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:

[tex]x = 36 + y\\y=x-36[/tex]

Now, plug this into the second equation:

[tex]7x + 16y = 574\\7x + 16(x-36)= 574\\7x+ 16x-586= 574\\23x=1150\\\\x=\dfrac{1150}{23}\\\\x=50[/tex]

Therefore, x is equal to 50.

Answer

50 individual tickets were sold.

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