# System of Equations Word Problem

by Charles
(Corning NY)

Five hats and three scarves cost \$99. While three hats and five scarves cost \$85. Find the cost of one hat.

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 Nov 25, 2014 Rating Re: Systems problem about hats and scarves NEW by: Anonymous Chapter: Sytem of Equations Word Problems Section: Questions from Other Students Question: Systems problem about hats and scarves In this problem, we are being asked to solve for the cost of one hat. Wouldn't X=15 be the cost of each hat? You have that X=15hats. I believe it's X=\$15/hat. However, I'm often wrong when it comes to algebra, so maybe I'm missing somehting here. Thank you.

 Dec 05, 2010 Rating System of Equations Word Problem by: Karin Hi Charles, For this type of problem, you will need to write a system of equations. A system of equations is two equations and the point of intersection is the solution. Let's first identify our variables. We will let: x = the number of hats y = the number of scarves. Step 1: Write two equations. 5x + 3y = 99 3x + 5y = 85 Now that we have two equations, we must choose a method for solving. The best method for this system is the linear combinations, or addition method. We will need to create one set of opposite terms. In order to create opposite terms, I will multiply the first equation by -5 and the second equation by 3. This will create opposite y terms and then the y terms will equal 0. -5(5x + 3y = 99) -25x - 15y = -495 3(3x + 5y = 85) 9x +15y = 255 So, now we have our two new equations: -25x - 15y = -495 9x +15y = 255 Now let's combine or add these two equations. -25x - 15y = -495 9x + 15y = 255 ------------------------ -16x = -240 Now divide both sides by -16 in order to solve for x. -16x/-16 = -240/-16 x = 15 Since x= the number of hats, we know that there are 15 hats. I hope this helps. You can find more examples at: https://www.algebra-class.com/systems-of-equations.html Karin

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