Respuesta :
The sum of the lemonade sold, the lemonade given to her cousins and
the amount left, gives the the amount of lemonade at the start.
Response:
- The volume of lemonade with Tiana at the start is 9.5 gallons
How are arithmetic operations performed with fraction?
Given:
The amount of lemonade Tiana sold at the sale = [tex]\dfrac{3}{4}[/tex]
The amount of lemonade Tiana gave to her cousins = [tex]\mathbf{\dfrac{3}{2}}[/tex] gallons
The amount of lemonade Tiana had left = [tex]\dfrac{7}{8}[/tex] of a gallon
Required:
The amount of lemonade, Tiana started with
Solution:
Let x represent the amount of lemonade Tiana started with, we have;
[tex]x = \mathbf{\dfrac{3}{4} \cdot x + \dfrac{3}{2} \ gallons + \dfrac{7}{8} \ gallons}[/tex]
[tex]\mathbf{x - \dfrac{3}{4} \cdot x} = \dfrac{3}{2} \ gallons + \dfrac{7}{8} \ gallons[/tex]
[tex]\dfrac{1}{4} \cdot x = \dfrac{3}{2} \ gallons + \dfrac{7}{8} \ gallons = \dfrac{19}{8} \ gallons[/tex]
[tex]x = \dfrac{19}{8} \ gallons \times 4 = \mathbf{9.5 \ gallons}[/tex]
- The volume of lemonade Tiana starts with is 9.5 gallons
Learn more about fractions here:
https://brainly.com/question/2194108
