Belt Auction

Solving linear systems graphically?

The owner of a mens clothing store bought 6 belts and 8 hats for $140. A week later, at the same prices, he bought 9 belts and 6 hats for $132. Find the price of a belt and the price of a hat.

Public Comments

1. 1. 6x+8y= 140 2. 9x+6y= 132 those are 2 equations we know are true. so take the second one, and make it 6y=132-9x then divide both sides by 6 and get y=22-1.5x now go back to the fist equation, and substitue "y" for (22-1.5x) 6x+8(22-1.5x)= 140 now there is only one variable, and we can solve the equation. 6x+176-12=140 6x+164=140 6x= -24 x= 4 and there's the first part of your answer. we know that belts cost $4, and 4 times 6= $24. 140-24= 116 116 divided by 8= 14.5 the hats cost $14.50 and the belts cost $4 you can double check it here: (4 times 6)+(14.50 times 8)= 140 24+116= 140 140=140 so the first one checks. (9 times 4)+(6 times 14.50)=132 36+87= 123 123=132.... oops. i did something wrong here but thats the basic idea. I'll go back and check my work and re post something when i figure out what i did wrong :D ______________________________________________________________________________________________ umm... I can't find what i did wrong here.. i should have worked. does anyone else see the problem?
2. Let x = price of a belt Let y = price of a hat 6x + 8y = 140 9x + 6y = 132 If you divide both sides of the 1st equation by 2 and divide both sides of the 2nd equation by 3, you can simply the equations to: 3x + 4y = 70 3x + 2y = 44 3x + 4y = 70 4y = -3x + 70 y = -3/4x + 35/2 3x + 2y = 44 2y = -3x + 44 y = -3/2x + 22 Graph both lines carefully; use graph paper or make sure to evenly space out the tick marks on the x and y axes as you draw them. Look for the intersection point of the lines on your graph then check your answer by plugging in for x and y into the two original equations. Final answer: (6,13) which means $6 for a belt and $13 for a hat ------------------------------------------------------------ To the previous poster, here's where you made the mistake: This step is correct: 6x+8(22-1.5x)= 140 However, you lost the x when distributing in the next step: 6x+176-12=140 It should be: 6x+176-12x=140 -6x + 176 = 140 -6x = -36 x = 6 (Also, when you solved 6x = -24, x would equal -4, not 4.)