Question

felicia pours juice from a carton into a glass. every time she fills the glass, the amount of juice in the carton changes by $-0.44$ l. she fills her glass $2\frac{3}{4}$ times in all. bernadette has a different carton of juice that is the same size. every time she fills her glass, the amount of juice in her carton changes by $-0.42$ l. she fills her glass $2\frac{2}{3}$ times in all. who has the greater total change in the amount of juice in their carton? show your work. explain your reasoning.

Explanation:

Step1: Convert mixed numbers to improper fractions

For Felicia: \(2\frac{3}{4}=\frac{2\times4 + 3}{4}=\frac{11}{4}\)
For Bernadette: \(2\frac{2}{3}=\frac{2\times3+ 2}{3}=\frac{8}{3}\)

Step2: Calculate the total change for Felicia

The total change for Felicia is \(-0.44\times\frac{11}{4}\).
First, \(0.44=\frac{44}{100}=\frac{11}{25}\), so \(-\frac{11}{25}\times\frac{11}{4}=-\frac{121}{100}=- 1.21\)

Step3: Calculate the total change for Bernadette

The total change for Bernadette is \(-0.42\times\frac{8}{3}\).
First, \(0.42=\frac{42}{100}=\frac{21}{50}\), so \(-\frac{21}{50}\times\frac{8}{3}=-\frac{168}{150}=-1.12\)

Step4: Compare the two values

Since \(-1.12> - 1.21\) (because when comparing two negative numbers, the one with a smaller absolute value is greater. \(\vert-1.12\vert = 1.12\) and \(\vert-1.21\vert=1.21\))

Answer:

Bernadette has the greater total change in the amount of juice in her carton.