Katie bought a dozen buttons for $2.52. How much was each button?

1 Answer
Dec 8, 2016

This is why the shortcut method used by Aiyan works

Explanation:

#color(blue)("Initial condition")#

12 buttons cost $2.52

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine the cost of each button")#

Write the given information as a ratio in fraction format. We need to find cost so use that as the numerator (top).

#("cost")/("count of buttons" ) -> ($2.52)/(12) " "=" "("cost of 1 button" )/1#

To change the 12 buttons into 1 button divide it by 12.

To keep the ratio in the correct proportion we also need to divide the top (numerator) by 12 as well:

#("cost")/("count")->($2.52)/12-=(color(red)($2.52-:12))/(12-:12) = ($0.21)/1#

#color(green)("The top number (numerator) of " color(red)($2.52-:12)" is where the ")##color(green)("shortcut comes from.")#

#("cost")/("count")-> ($0.21)/1#

So 1 button costs $0.21