Answer:
The recipe is enough for Lucy and 3 friends.
And [tex]=3\frac{10}{12}[/tex] cups of smoothie remains after Lucy gives one of her friends 3/4 cups of smoothie.
Step-by-step explanation:
There is a mistake in the question the quantity of yogurt should be 1 1/2 cup.
Given:
Lucy is making a smoothie using ingredients:
1 1/3 cups banana = 4/3 cups banana.
1/2 cup yogurt = 3/2 cups yogurt.
1 cup strawberries.
3/4 cup orange juice.
Now, to find will this recipe make enough for Lucy and 3 friends to have 1 cup of smoothie and quantity of smoothie remains after Lucy gives one of her friends 3/4 cups of smoothie.
So, we add the given ingredients to get the total quantity of smoothie:
[tex]\frac{4}{3} +\frac{3}{2} +1+\frac{3}{4}[/tex]
Taking the same denominator we get:
[tex]=\frac{16+18+12+9}{12}[/tex]
[tex]=\frac{55}{12}[/tex]
[tex]=4\frac{7}{12} .[/tex]
Thus, [tex]=4\frac{7}{12}[/tex] is enough for Lucy and 3 friends to have 1 cup of smoothie.
Now, to get the smoothie remains after Lucy gives one of her friends 3/4 cups of smoothie:
Subtracting 3/4 cups of smoothie from the total quantity of smoothie:
[tex]\frac{55}{12} -\frac{3}{4}[/tex]
[tex]=\frac{55-9}{12}[/tex]
[tex]=\frac{46}{12}[/tex]
[tex]=3\frac{10}{12}[/tex]
Therefore, the recipe is enough for Lucy and 3 friends. And [tex]=3\frac{10}{12}[/tex] cups of smoothie remains after Lucy gives one of her friends 3/4 cups of smoothie.
