Question 176133: Hi there. I'm currently trying to complete an assignment and the first question has me stumped. I've tried looking up how to do it, tried ratio etc and can't for the life of me work out the formula I'm meant to use. The question as printed is as follows:
'A commercial developer is considering three brown field sites on the perimeter of Leeds city centre. All plots are being sold by Leeds City Council at prices such that plot A is £20 000 less than plot B, and plot B is £ 30 000 more than plot C. The sale of the three plots will generate an income of £3 190 000 for the council. Determine the sale price for each plot.'
Thanks in advance for your help.
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! i'll work in thousands and then translate back at the end.
20,000 = 20 thousand pounds
30,000 = 30 thousand pounds
3190,000 = 3190 thousand pounds
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A = B - 20
B = C + 30
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you want to reduce the number of unknowns as much as possible, winding up with only 1 if possible.
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looks like you may be able to get everything in terms of C.
let's see if we can do that.
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you have B = C + 30
you have A = B - 20
since B = C + 30, then the second equation can be rewritten as:
A = (C + 30) - 20
which becomes:
A = C + 10
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you now have everything in terms of A.
your equation of A + B + C = 3190 becomes:
C + 10 + C + 30 + C = 3190
combine like terms and it becomes:
3*C + 40 = 3190
subtract 40 from both sides and it becomes:
3*C = 3150
divide both side by 3 and it becomes:
C = 1050
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since C = 1050, this makes:
A = 1060
B = 1080
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A + B + C = 1060 + 1080 + 1050 = 3190
this matches the original total so this is good.
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A = 1060
B = 1080
A = B - 20
this matches the original assumption so this is good.
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B = 1080
C = 1050
B = C + 30
this matches the original assumption so this is good.
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answer is:
sale price of each plot is:
A = 1060,000 pounds.
B = 1080,000 pounds.
C = 1050,000 pounds.
total is 3190,000 pounds.
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