4 liters of punch can serve 16.
5 liters of punch will be needed for 20 servings.
7 liters of punch will serve 28.
Step-by-step explanation:
Given,
Ratios of liters of punch to servings = 2:8
Let,
x be the servings for 4 liters.
New ratio of liters of punch to servings = 4:x
Using proportion;
Ratio :: New ratio
[tex]2:8::4:x[/tex]
Product of mean = Product of extreme
[tex]8*4=2*x\\32=2x\\2x=32[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{32}{2}\\x=16[/tex]
4 liters of punch can serve 16.
Let,
y be the liters of punch for 20 servings.
New ratio = y:20
Using proportion;
[tex]2:8::y:20[/tex]
Product of mean = Product of extreme
[tex]8*y=20*2\\8y=40\\[/tex]
Dividing both sides by 8
[tex]\frac{8y}{8}=\frac{40}{8}[/tex]
y=5
5 liters of punch will be needed for 20 servings.
Let,
z be the number of servings for 7 liters of punch.
New ratio = 7:z
Using proportion
[tex]2:8::7:z\\[/tex]
Product of mean = Product of extreme
[tex]8*7=2*z\\56=2z\\2z=56[/tex]
Dividing both sides by 2
[tex]\frac{2z}{2}=\frac{56}{2}\\z=28[/tex]
7 liters of punch will serve 28.
Keywords: ratio, proportion
Learn more about ratios at:
- brainly.com/question/2154850
- brainly.com/question/2367554
#LearnwithBrainly
