Question

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?

Answer 1

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 2

60 liters fruit juice.

40 liters ginger ale.

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:

`g+f=100...(1)`

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:

`g+1.50f=130...(2)`

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

`g=100-f`

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

`100-f+1.50f=130`

`100+0.50f=130`

`100-100+0.50f=130-100`

`0.50f=30`

`(0.50f)/(0.50)=(30)/(0.50)`

`f=60`

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

Now, we will substitute
`f=60` in equation (1).

`g+60=100`

`g+60-60=100-60`

`g=40`

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