A 24 pack of soda costs $8 each and bags of chips cost $6 each. You have $120 to spend and there is a 16 items or fewer fast lane open. How many sodas should you purchase to spend all the money and be able to use that fast lane?
To solve this problem, we need to find the number of sodas you can purchase while spending all your money and ensuring that you can use the fast lane with 16 items or fewer.
Let's assume you purchase x sodas. We know that each soda costs $8. Therefore, the cost of x sodas would be 8x dollars.
You also want to purchase bags of chips. Each bag of chips costs $6. If you subtract the cost of sodas from your total budget of $120, you can determine how much money you have left to spend on chips.
Total budget - Cost of sodas = Remaining budget
$120 - 8x = Remaining budget
Now, let's determine how many bags of chips you can purchase. Divide the remaining budget by the cost of each bag of chips:
Remaining budget / Cost of chips = Number of bags of chips
Remaining budget / $6 = Number of bags of chips
We want to spend all the money, so the expression for the remaining budget should be zero:
$120 - 8x = 0
Now we can solve for x:
120 - 8x = 0
8x = 120
x = 120 / 8
x = 15
Since we can't purchase fractions of a soda, you should buy 15 sodas. This will still leave you with $120 - 8 * 15 = $0 for purchasing chips. Therefore, you will be able to use the fast lane with 16 items or fewer.