Help I’m so lost in Math

Question

3.99 for 12-355ml cans, 1.79 for 2L bottle, or 4.99 for 6-710ml bottles. There are 50 ppl drinking aprox 16 ounces of pop each. How much should I buy and which is the best value?

Answer 1

Let's start off by converting all of our volumes to the same unit. I chose to use liters. Here are the values we'll need to convert: a. 355 ml; b. 710 ml; and c. 16 ounces (oz)

a. 1,000 ml = 1 L, so you can convert 355 ml to liters by dividing this value by 1,000 ml and multiplying it by 1 L. By dividing 355 ml by 1,000 ml, we're canceling out the ml unit; Lastly, by multiplying by 1L, we've applied our conversion formula (1,000 ml = 1L) and successfully converted our volume from milliliters to liters:

355 ml = 0.355 L

b. Similarly, we can convert 710 ml to liters by dividing by 1,000, or moving the decimal point three places to the left:

710 ml = .710 L

c. Now this last conversion is a little trickier... There are 33.814 fluid ounces in a liter, so our new conversion formula is: 33.814 oz = 1 L

...Divide our 16 oz by 33.814 oz and multiply by 1 L:

16 oz = 0.47 L

Ok, now we're ready to find the best deal! Here are our options:

1. option i. $3.99 for 12 cans; each can is 0.355 L
2. option ii. $1.79 for one large bottle; each large bottle is 2 L
3. option iii. $4.99 for 6 small bottles; each small bottle is .710 L

We can use the following formula to calculate the price per volume for each of our options:

price = number(volume)

1. option i.

$3.99 = 12(0.355L)

--> $3.99 = 4.26L

** Divide both sides by 4.26 to isolate L**

--> $3.99 / 4.26 = 4.26 L / 4.26

--> $0.94 = 1 L

option i costs $0.94 per liter

1. option ii.

$1.79 = 1 (2 L)

--> $1.79 / 2 = 2 L / 2

--> $0.90 = 1 L

option ii costs $0.90 per liter

1. option iii.

$4.99 = 6(0.710 L)

--> $4.99 = 4.26 L

--> $4.99 / 4.26 = 4.26 L / 4.26

--> $1.17 = 1 L

option iii costs $1.17

After comparing the price per volume of our three options, we now know that option ii (the 2L large bottle for $1.79) is our best deal.

Now that we know which option's the cheapest, we can figure out how much of it we want to buy. To do this, let's first figure out how many liters our guests will likely drink. Recall that we are serving 50 people, each expected to consume 16 oz, or 0.47 L of soda. To find our estimated total volume, multiply 50 by 0.47:

50(0.47 L) = 23.5 L

That means we have to purchase at least 23.5 L. Since we're purchasing whole liters--not half liters-- we can round up our estimated total volume to 24 L. To find out how many 2 L bottles we'll need to purchase, divide our estimated volume intake by the volume of the bottles we're purchasing:

24 L / 2 L = 12 bottles

Since each 2 L bottle is $1.79, to find the total price, multiply the price per bottle by the number of bottles needed:

$1.79(12) = $21.48

Final answer: The best deal is the 2 L bottles for $1.79 each. We'll need 12 of them, which will cost us $21.48