Answer: 480 acres
Step-by-step explanation:
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.
