Answer:
She put 60 liters of fruit juice and 40 liters of ginger ale in a 100 liters punch.
System of equations matches the situation:
g+f = 100 liters
$g+$1.50f=$130
Step-by-step explanation:
Let 100 liters of punch contains g liters of ginger ale and f liters of fruit juice
i.e. g+f = 100 liters ---(a)
We are given the cost of the ginger ale is $1 per liter and the fruit juice is $1.50 per liter
So, cost of g liters ginger ale is $g.
and cost of f liters of fruit juice is $1.50f .
Sharon spent a total of $130 on 100 liters punch.
Thus total cost of 100 liters punch = cost of f liters of fruit juice +cost of g liters of ginger ale.
⇒$g+$1.50f=$130 ---(b)
solving (a) and (b)
from (a) g+f = 100
g= 100-f
substitute this value of g in (b) gives
⇒![100-f+1.50f=130](https://tex.z-dn.net/?f=100-f%2B1.50f%3D130)
⇒![100+0.50f=130](https://tex.z-dn.net/?f=100%2B0.50f%3D130)
⇒![0.50f=130-100](https://tex.z-dn.net/?f=0.50f%3D130-100)
⇒![0.50f=30](https://tex.z-dn.net/?f=0.50f%3D30)
⇒![f=\frac{30}{0.50}](https://tex.z-dn.net/?f=f%3D%5Cfrac%7B30%7D%7B0.50%7D)
⇒![f=60](https://tex.z-dn.net/?f=f%3D60)
Thus 60 liters of fruit juice she put in a 100 liters punch
putting value of f =60 in (a)
we get
⇒![60+g=100](https://tex.z-dn.net/?f=60%2Bg%3D100)
⇒![g=100-60](https://tex.z-dn.net/?f=g%3D100-60)
⇒![g=40](https://tex.z-dn.net/?f=g%3D40)
Thus 40 liters of ginger ale she put in a 100 liters punch