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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
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
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:



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