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Sharon is making 100 liters of punch for a party. The punch contains ginger ale (g) and fruit juice (f). The cost of the ginger ale is $1 per liter and the fruit juice is $1.50 per liter. If Sharon spent a total of $130, how many liters of each did she put in the punch? Which system of equations matches the situation?

Respuesta :

g+f=100liters
$1g + $1.5f = $130 

g=130-1.5f  substitute into first equation for g

(130-1.5f)+f=100
130-.5f=100
-.5f=100-130
-.5f=-30
f=-30/-.5
f= 60 liters of fruit juice

substitute into first equation

g+60 = 100liters
g=100-60
g=40 liters of ginger ale

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


⇒[tex]100-f+1.50f=130[/tex]


⇒[tex]100+0.50f=130[/tex]


⇒[tex]0.50f=130-100[/tex]


⇒[tex]0.50f=30[/tex]


⇒[tex]f=\frac{30}{0.50}[/tex]


⇒[tex]f=60[/tex]


Thus 60 liters of fruit juice she put in a 100 liters punch

putting value of f =60 in (a)

we get


⇒[tex]60+g=100[/tex]


⇒[tex]g=100-60[/tex]


⇒[tex]g=40[/tex]


Thus 40 liters of ginger ale she put in a 100 liters punch

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