# Using Linear Equations To Solve Word Problems

The system is: x y = 100, (1) ("100 tickets were sold") and 4x 2.5y = 355.

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That equation should look like this: x y = 16 The second piece of information we have is that the total number of legs in the farmhouse is 60.

Since we know that cows have four legs each and chickens have two legs each, we have enough information to make another equation.

Now, this task gave us enough information to make two equations.

The first one is that the sum of the number of chickens (x) and the number of cows (y) is 16, since there are only 16 animals in the farmhouse.

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 will get a single equation for y: 4*(100 - y) 2.5y = 355. Simplify and solve it: 400 - 4y 2.5y = 355, or -1.5y = 355 - 400, -1.5y = -45, y = = 30. 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. This one will look like this: 2*x 4*y = 60 Now we have a system of linear equations with two equations and two variables.The only thing left to do now is to solve the system.How many rolls of each kind of gift wrap were sold?Solution Let x be the unknown number of gift wrap in solid colors and y be the unknown number of print gift wraps.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.

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