Question

They paid $72.94 for 6 pounds of steak. What was the price per pound?

Answer 1

This a division question, the opposite of multiplying.

Explanation:

`$72.94div6=$12.1566...=$12.15 2/3~~$12.16`

Check!
`6xx$12.16=$72.96`

This does not come out exactly right, but close enough?

Answer 2

Meneer showed you the shortcut method. This is why it works.

`1^("lb")` approximately costs $12.16 to 2 decimal places

Explanation:

Using ratio

`("cost")/("quantity") ->($72.94)/6^("lb") =("cost")/(1^("lb"))`

So we need to change the `6^("lb")" into "1^("lb")`

In fractions or ratios for multiply or divide, what you do to the bottom you do to the top to maintain the same ratio.

`(color(red)($72.94-:6))/(6^("lb")-:6) =("cost")/(1^("lb"))`

`color(red)("Now you can see where the shortcut "$72.94-:6" comes from.")`

cost for `1^("lb")" is "$12.15666.....` as an approximate value

As a precise value this is `$12 47/300`