The answer is: Two (2) weeks.
_____________________________________
Explanation:
_____________________________________
Anne has:
_________________
¾ of a bag; or ¾(1b); or, (¾)b ; which: b = number of bags of cat food.
_________________
Anne's furry and purry little friend eats:
___________________________________
[(⅜)b] / wk ; in which: "wk" = weeks(s).
___________________________________
So, how many "weeks"; or, "wk", will the cat food last? We want our answer to be in "wk".
____________________________________
→ {1 wk / [(⅜)b] } [(¾)b] = ? wk. ?
___________________________________
→ The unit symbols, "b", cancel to "1"; and we have:
__________________________________
→ [1 wk (¾)] / [(⅜)] = [(¾) wk] / [(⅜)]
_________________________________
→ = [(¾) / (⅜)] wk.
_________________________________
→ \(\frac{3}{4}\) ÷ \(\frac{3}{8}\)
_________________________________
→ = \(\frac{3}{4}\) \(\frac{8}{3}\) ;
______________________________________________
→ The "3's" 'cancel out. to "1's".
The "4" change, and the "8" changes to a "2" (since "8÷4 = 2").
______________________________________
→ And we are left with:
_________________________________________
→ \(\frac{1}{1}\) \(\frac{2}{1}\) ;
_________________________________________
→ = 1 2
_________________________________________
= 2 wks. ; → The answer is: Two (2) weeks.
_________________________________________
