# Using Linear Equations To Solve Word Problems

So, our problem is reduced to the solution of the linear system of two equations in two unknowns .

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If 100 tickets were sold for \$355.00, how many tickets were adult tickets?

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

You have for the first equation left side, and for the second equation left side. Each apple costs 20 cents and each orange costs 10 cents.

Tickets are sold at \$4.00 for adults and \$2.50 for students.

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.Since the total amount of money collected was 40, the second equation is .So, we reduced our problem to the solution of the linear system of two equations in two unknowns . Open parentheses, collect common terms, and step-by-step simplify: , , , . Solution When they ask "Determine percentage of gold", they mean the ratio of the gold contents by The volume of a piece of metal is (12 in x 6 in x 4 in) = 288 cubic inches. Now, having the densities expressed in consistent units, you can write the equation.So, we just found y, the number of student tickets. Many word problems Involving unknown quantities can be translated for solving quadratic equations Methods of solving quadratic equations are discussed here in the following steps. Step II: use the conditions of the problem to establish in unknown quantities.Step III: Use the equations to establish one quadratic equation in one unknown.Step IV: Solve this equation to obtain the value of the unknown in the set to which it belongs.x = -5 does not satisfy the conditions of the problem length or breadth can never be negative. In solving a problem, each root of the quadratic equation is to be verified whether it satisfies the conditions of the given problem. 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 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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