A farm has 76 acres of wheat. The farmer can harvest the wheat from 12 acres per day. In how many days will all of the fields be harvested?

1 Answer
Tony B
Oct 22, 2016

#6 1/3 # days

Explanation:

Let the unknown number of days be #x#
#color(white)(.)#
#color(blue)("Using ratio to show why the shortcut method works.")#

#(76" acres")/(12" acres") =(x" days")/(1" day")#

so #x=76/12 ->(76-:4)/(12-:4)=19/3 = 6 1/3" days"#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Using ratios differently")#

The clue is in the wording of 'acres per day' which translates to:
#("acres")/("days")#

#(12" acres")/(1" day")=76/x#

To maintain the correct ration, if you multiply the top number of a fraction or ratio you must do the same to the bottom number
Note that #6 1/3xx12=76#

Multiply by 1 but in the form of #1=(6 1/3)/(6 1/3)#

#[(12" acres")/(1" day")xx1] =76/x#

#[(12" acres")/(1" day")xx(6 1/3)/(6 1/3)]=76/x#

#76/(6 1/3)=76/x#

#x=6 1/3" days"#

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