If .20 bushel is 1 dozen apples and a dozen apples has a mass of 2.0 kg, what is the mass of 0.50 bushel of apples?

1 Answer
May 17, 2016

Mass of #0.5# bushel of apples = #5 kg#

Explanation:

This problem can be solved in 2 ways:

Method 1:

We have #0.2" bushel" = 1 doz = 2 kg#

#=> 0.2" bushel" = 2 kg#

#=> 1" bushel" = 2/0.2 kg=(2color(red)(0))/(0cancel(.)2) kg=20/2kg#

#=> 1" bushel" = 10 kg#

#=> 0.5" bushel" = 10xx0.5 kg#

#=> 0.5" bushel" = 5 kg#

Method 2:

  • First, we find the number of apples in #0.5# bushel.

We have,

#0.20" bushel" = 1 " doz apples" = 12 " apples"#

#=>1" bushel"= 12/0.20#

We need to get a #1# or a multiple of #10# in the denominator.

We know that #0.20 xx 5 = 1#
Multiply the numberator and denominator by 5.

Then, #(12xx5)/(0.20xx5)= 60/1#

#=>1" bushel"= 60 " apples"#

#=>0.5" bushel"= 60xx0.5=30 #

Therefore, #color(red)(0.5 " bushel" = 30" apples"#

  • Next we calculate the mass of these apples:

Mass of #12 " apples" = 2 kg#

Mass of #1 " apples" = 2/12 kg#

Mass of #30 " apples" = (2xx30)/12 kg#

#= (2xxcancel30^color(red)(10))/cancel12^color(red)(4) kg#

#= (2xxcancel10^color(red)(5))/cancel4^color(red)(2) kg#

#= (cancel2xx5)/cancel2 kg#

Mass of #30 " apples" = 5 kg#