Question

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

Answer 1

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.

Answer 2

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`