# Using Linear Equations To Solve Word Problems

In this lesson we present some typical word problems and show how to solve them using linear systems of two equations in two unknowns.The Madison Local High School marching band sold gift wrap to earn money for a band trip to Orlando, Florida.The system is: x y = 100, (1) ("100 tickets were sold") and 4x 2.5y = 355.

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Keep the first equation as is and multiply the second equation by two: , Subtract the second equation from the first one: , .

Now, substitute the found value of into the first equation and calculate : , , , . Check Substitute these values of and into the first and the second equations.

When it comes to using linear systems to solve word problems, the biggest problem is recognizing the important elements and setting up the equations.

Once you do that, these linear systems are solvable just like other . The best way to get a grip around these kinds of word problems is through practice, so we will solve a few examples here to get you accustomed to finding elements of linear systems inside of word problems.

Since the total number of rolls sold was 480, the first equation is .

Now, the total cost of x gift wraps in solid colors sold for .00 per roll is equal to dollars, while the total cost of y print gift sold for .00 per roll is equal to dollars.

If 100 tickets were sold for 5.00, how many tickets were adult tickets?

Solution Let "x" be the numbers of adult tickets, and let "y" be the numbers of student tickets.

The gift wrap in solid colors sold for .00 per roll, and the print gift wrap sold for .00 per roll.

The total number of rolls sold was 480, and the total amount of money collected was 40.

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