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Question 943749: A group of farmers planned to clean 80 acres of wheat per day to finish the work on schedule. Right before the work started, they received a new piece of machinery that helped them clean 10 more acres per day than originally planned. As a result of increased productivity in the last day before the deadline they only had to clean 30 acres. How many acres of wheat did the group of farmers have to clean?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i think i understand the problem.
if so, then the solution is as follows:
let x = the number of days required to finish the job.
let y = number of acres that had to be cleaned.
without the new machine, the formula would be:
80x = y
that means cleaning 80 acres per day * x days will equal y acres that are cleaned.
with the new machine, the formula would be:
90(x-1) + 30 = y
that means cleaning 90 acres per day for one less day and then cleaning 30 acres on the last day will equal y acres that are cleaned.
so you have 2 equations.
80x = y
90(x-1) + 30 = y
replace y in the second equation with the value of y from the first equation gets you:
90(x-1) + 30 = 80x
solve for x to get:
x = 6
what this means is:
80 acres a day for 6 days will equal 480 acres that are cleaned.
90 acres a day for 5 days and then 30 acres on the last day will equal 480 acres that are cleaned.
with the old machine we are looking at:
80 + 80 + 80 + 80 + 80 + 80 = 480.
with the new machine we are looking at:
90 + 90 + 90 + 90 + 90 + 30 = 480.
looks like they had to clean 480 acres.
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