problem solving
posted by ben on .
You need to put a carpet in a rectangular room that measures 13 feet by 22 feet as a cost of $19.50 per square yard. Assuming that you can buy precisely the amount of carpet you need, how much will the carpet for the room cost? Demonstrate stepbystep solution.
I got $1,858.9999. is that right?

19.5 $/y^2 * 1 y^2/9ft^2 = (19.5/9)$/ft^2
13 ft * 22 ft = 286 ft^2
286 ft^2 * (19.5/9) $/ft^2 = 619.67dollars 
approximate in head to see if reasonable
15 * 20 = 300 ft^2
about 10 ft^2 / yard^2 (nine is about ten)
so about 30 y^2
* 20 = 600 dollars 
Okay I was dividing by 3 instead of 9. Got it now, thanks.

1 yd^2(3 ft/1yd)(3 ft/1 yd) = 9 ft^2/yd^2

always multiply by things that are the same top and bottom so the units come out (you are really always multiplying by one)
for example
3600 seconds is the same as 1 hour
so
3600 s/1 hr
is the same top and bottom
and
1 hr/3600 s
is the same top and bottom
same deal with 1 ft/12 in
or 12 in / 1 ft
or 1 mi / 5280 ft
or 5280 ft/ 1 mi
( if using landlubber miles )
or 16 oz /lb or 1 lb/16 oz
etc 
Just get that idea in your head and these are easy.

Maria earns d dollars and owes $850 in expenses. How much, in dollars, does she have left after paying for expenses?

d850