Cost per ounce for orange juice doesn't add up

Question

I was at the store and there were two bottles of Orange Juice.

The first was 59 oz and cost $3.49 (16.9 cents per oz)
The second was 128 oz and cost $6.49 (19.7 cents per oz)

That's straight forward enough but if I buy two of the smaller 59oz containers (118 oz total) I end up paying $6.98 which gives me 10 oz less than the big container and costs me 49 cents more (but is still just 16.9 cents per oz)

Why doesn't this add up to be a linear savings when buying multiple small containers?

Could you clarify what is a non-linear function of what (number of ounces? number of small containers?) and how your calculation shows this? — Trevor Wilson, May 07 '13 at 20:02

score 3 · Answer 1 · answered May 07 '13 at 19:48

3

Because you calculated ounces per cent, not cents per ounce. The 59 oz bottle is $3.49 / 59 oz = $0.059 per ounce. The 128 oz bottle is $6.49 / 128 oz = $0.051 per ounce.

The better deal is the bigger bottle.

answered May 07 '13 at 19:48

David T Wilcox

31

Thanks, I should have looked at my units. – Justin Garrison May 07 '13 at 22:54

score 3 · Accepted Answer · answered May 07 '13 at 19:48

3

The smaller container costs $\frac{349}{59}=5.9$ cents per ounce, while the larger one $\frac{649}{128}=5.1$ cents per ounce, correct to $1$ decimal place.

answered May 07 '13 at 19:48

Cost per ounce for orange juice doesn't add up

2 Answers2