Question

A group of farmers planned to harvest 80 acres of wheat per day to finish their work on schedule. Right before the work started, they received a new piece of machinery that helped them to harvest 10 more acres per day than originally planned. On the last day before their deadline, they only had to harvest 30 acres due to their increased productivity. How many acres of wheat did the group of farmers have to harvest?.

Answer 1

480 acres ig

Explanation:

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.