Answer to Question #143043 in Algebra for jion

Question

Cinderella has 1/4 as many bottles of magic

as her sister. In total, they had 30. How many

bottles of magic does each person have?

Define your variables and solve.

Answer 1

$\displaystyle\textsf{Let the bottles of magic of Cinderella be}\, x\\ \textsf{Cinderella's sister bottle of magic is}\, x + \frac{x}{4}\\ x + x + \frac{x}{4} = 30\\ \frac{9x}{4} = 30\\ x = \frac{30 \times 4}{9} = \frac{40}{3} = 13.3\\ \textsf{Putting the values of}\, x,\\\textsf{we have the bottle of magic}\\\textsf{each person has.}\\ \textsf{Cinderella's sister bottle of magic is}\, \frac{40}{3} + \frac{40}{4\times 3} = \frac{50}{3} = 16.7.\\ \therefore \,\textsf{Cinderella has}\, 13.3\, \textsf{bottles of magic}\,\&\\ \textsf{Cinderella's sister has}\, 16.7\, \textsf{bottles of magic.}$