Question 468085: Here is the question I have to answer: "A rectangular field is 4 times as long as it is wide. Let the width be x and the length will therefore be 4x. If the length is decreased by 10 in. and the width is increased by 2 in. the perimeter will be 80 in. Find the dimensions of the original field."
In the end I have to come up with two answers; the length and the width.
I tried doing the problem in a few different ways, if I need to give you all of my tries, please tell me so. But I'll just give you my latest try which I think might be partially right at the very least.
2(4x-10)+2(2+x)=80
8x-10+3x=80
5x-10=80
90/5=18
Is that part right or no? If not do I at least have the right idea? and your answers aren't supposed to come out as fractions are they?
NOTE:Please do not give me the answers, but just try to show me how to work this problem.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you have the right idea, but your calculations are off.
here's what you did:
2(4x-10)+2(2+x)=80
8x-10+3x=80
5x-10=80
90/5=18
you were good at:
2(4x-10) + 2(2+x) = 80
you screwed up at 8x-10+3x = 80
here's what you should have done:
2(4x-10) = 2*4x - 2*10 = 8x-20
2(2+x) = 2*2 + 2*x = 4+2x
you should then have gotten:
8x - 20 + 4 + 2x = 80
you would then have combined like terms to get:
10x - 16 = 80
you would then have added 16 to both sides of the equation to get 10x = 96
you would have divided both sidesof the equatilon by 10 to get x = 9.6
your answer should have been 9.6
to confirm that's a good answer, we'll replace x in the original equations with 9.6 and see if those equations are true.
you started with L = 4x and W = x
that makes L = 4*9.6 and W = 9.6
that makes L = 38.4 and W = 9.6
you then subtracted 10 from L to get 28.4
you then added 2 to W to get 11.6
your perimeter is 2*L + 2*W which becomes 2*28.4 + 2*11.6 which becomes 56.8 + 23.2 which becomes 80.
the value of x = 9.6 is good.
here's a reference on the laws of addition and multiplication that might be helpful.
check out the distributive law of multiplication over addition.
this is where you started to go wrong in your calulations.
http://www.bymath.com/studyguide/ari/ari4.html
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