Sharon is making 100 liters of punch for a party. The punch contains ginger ale (g) and fruit juice (f). The cost of 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?

100 = g + f
130 = 1g + 1.5f

f = 12
because u can use elimination by multiplying equation 2 by -1 to cancel out g variable then combine both equations
g = 88
because plug in f's value of 12 to 1st equation then subtract 12 from each side

Answer Link

ApusApus ApusApus · Answer 2 · 2019-05-24T11:53:55+02:00

Answer:

60 liters fruit juice.

40 liters ginger ale.

Step-by-step explanation:

Let g represent ginger ale and f represent fruit juice.

We have been given that Sharon is making 100 liters of punch for a party. The punch contains ginger ale (g) and fruit juice (f). We can represent this information in an equation as:

[tex]g+f=100...(1)[/tex]

The cost of ginger ale is $1 per liter and the fruit juice is $1.50 per liter. Sharon spent a total of $130.

We can represent this information in an equation as:

[tex]g+1.50f=130...(2)[/tex]

Now, we will use substitution method to solve system of equations. From equation (1) we will get,

[tex]g=100-f[/tex]

Substituting this value in equation (2) we will get,

[tex]100-f+1.50f=130[/tex]

[tex]100+0.50f=130[/tex]

[tex]100-100+0.50f=130-100[/tex]

[tex]0.50f=30[/tex]

[tex]\frac{0.50f}{0.50}=\frac{30}{0.50}[/tex]

[tex]f=60[/tex]

Therefore, Sharon put 60 liters of fruit juice in the punch.

Now, we will substitute [tex]f=60[/tex] in equation (1).

[tex]g+60=100[/tex]

[tex]g+60-60=100-60[/tex]

[tex]g=40[/tex]

Therefore, Sharon put 40 liters of ginger ale in the punch.