Please answer ASAP and if you do you will get Brainliest. Catherine buys a gallon of ice cream from the store. After taking it home, she eats a fifth of a gallon of ice cream. Her sister eats some of the ice cream as well. If two-thirds of the original amount of ice cream is left, then what fraction of a gallon of ice cream did her sister eat?

Accepted Solution

Answer:Catherine's sister ate 2/15 gallons of the ice cream.[tex]\displaystyle \frac{2}{15}[/tex].Step-by-step explanation:Let [tex]x[/tex] be the amount of ice cream that Catherine's sister ate, in gallons.Original amount: 1 gallon.What Catherine ate: [tex]\displaystyle \frac{1}{5}[/tex] gallons.What Catherine's sister ate is assumed to be [tex]x[/tex] gallons.What's left: [tex]\displaystyle \frac{2}{3}[/tex] gallons.Consider the relationship:[tex]\text{Original amount - What Catherine ate - What Catherine's Sister ate}\\ =\text{ What's left.}[/tex].That is:[tex]\displaystyle 1- \frac{1}{5} - x = \frac{2}{3}[/tex].Add [tex]x[/tex] to both sides of this equation:[tex]\displaystyle 1 - \frac{1}{5} = \frac{2}{3} +x[/tex]Substract [tex]\displaystyle \frac{2}{3}[/tex] from both sides:[tex]\displaystyle 1 - \frac{1}{5} - \frac{2}{3} = x[/tex].Convert the denominator of all three numbers on the left-hand side to [tex]3 \times 5 = 15[/tex][tex]\displaystyle \frac{15}{15} - \frac{3}{15} - \frac{10}{15} = x[/tex].[tex]\displaystyle x = \frac{2}{15}[/tex].In other words, Catherine's sister ate [tex]\displaystyle \frac{2}{15}[/tex] gallons of the ice cream.