A bag of potatoes weighing 5 pounds and 12 ounces cost $2.07. What is the cost of 1 pound of potatoes?

2 Answers
Jun 9, 2016

One pound of potatoes cost #$0.36# or #36# cents.

Explanation:

As one pound is equal to #16# ounces, we can write #5# pounds and #12# ounces as #5 12/16=5 3/4=23/4# pounds.

Now #23/4# pounds of potatoes cos #$2.07=207/100#

Hence, one pond of potatoes cost #(207/100)/(23/4)#

= #207/100xx4/23#

= #(9cancel207)/100xx4/(1cancel23)#

= #36/100=0.36#

Hence, one pound of potatoes cost #$0.36# or #36# cents.

Jun 9, 2016

Another approach. Really it is the same thing in disguise!

#$0.36#

Explanation:

To start with this be the same as the other solution. Will very slightly change in the middle. Then end up the same again.
The important thing to remember is that #16 oz = 1 lb#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Given weight #" "5color(white)(.) lb" " +" " 12/16color(white)(.)lb#

This is the same as #5 3/4 color(white)(.)lb -> 5.75color(white)(.)lb#

The cost is #$2.07# so as a ratio we have:

#($2.07)/(5.75color(white)(.)lb)#

But we need the cost for #1color(white)(.)lb#

Let the unknown cost be #x#, then by the law of ratios we have

#($2.07)/(5.75color(white)(.)lb) -= x/(1color(white)(.)lb)#

But #x/1# is the same as just having #x# so

#x=($2.07)/(5.75color(white)(.)lb)" "=" "$0.36#