7-11 mini-mart started a promotion where you can buy a refillable 40 oz. Soda for a one-time price $6.00, then fill the cup for $0.79 per year for a year or you can buy their filled disposable 32 oz. Soda cup for $1.69. How many sodas do you need to buy to make it work buying the refillable cup?

7 cups of soda

Step-by-step explanation:

If we call the number of cups you buy by "x", we have that the price for the refillable cup P1 is:

P1 = 6 + 0.79*x

And the price for the other option is:

P2 = 1.69*x

To find how many sodas do you need to buy to make it work buying the refillable cup, you just need to equate the two prices and find the value of x:

P1 = P2

6 + 0.79*x = 1.69*x

0.9*x = 6

x = 6/0.9 = 6.6667 cups

So, you need to buy at least 7 cups of soda to make the refillable cup worth it.