Solve: -- Determine the values for x by completing the steps shown.
2 answers:
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<h2>Word Problem</h2>
To form equations from word problems, we can do the following:
- Identify variables
- Find key information
- Identify word equations and translate into numerical equations
- Solve
We're given:
- Let <em>x</em> be the number of individual tickets that were sold
- Let <em>y</em> 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 <em>x</em>?)
Here are all the equations we have created:
- x = 36 + y
- 7x + 16y = 574
We can solve for the value of <em>x</em> using systems of equations.
First, isolate <em>y</em> in the first equation:
Now, plug this into the second equation:
Therefore, <em>x</em> is equal to 50.
<h2>Answer</h2>50 individual tickets were sold.