Answer:
Carmen can make [tex]10\frac{5}{16}[/tex] full servings.
Step-by-step explanation:
Given : Carmen mixes [tex]3\frac{1}{2}[/tex] cups of water with [tex]3\frac{3}{8}[/tex] cups of juice to make punch.
Total quantity of punch Carmen made = total cup of water + cup of juice she mixes
Total quantity of punch Carmen made = [tex]3\frac{1}{2}+3\frac{3}{8}[/tex]
Solving , we get,
Total quantity of punch Carmen made = [tex]\frac{7}{2}+\frac{27}{8}[/tex]
taking LCM(2,8) = 8 , we get,
Total quantity of punch Carmen made = [tex]\frac{28+27}{8}=\frac{55}{8}[/tex]
Also, given She pours [tex]\frac{2}{3}[/tex] cup servings of punch.
Thus, [tex]\frac{2}{3}[/tex] cup of mixture makes 1 serving cup.
Using unitary method,
In unitary method we first find the value of a single quantity and then multiply it with the desired quantity.
1 cup of mixture makes [tex]\frac{3}{2}[/tex] serving cup.
[tex]\frac{55}{8}[/tex] cup makes = [tex]\frac{3}{2}\times\frac{55}{8}[/tex]
[tex]\frac{55}{8}[/tex] cup makes = [tex]\frac{165}{16}=10\frac{5}{16}[/tex]
Thus, She can make [tex]10\frac{5}{16}[/tex] full servings.
