rates question

[mathguy]

Hi everyone, I'm totally lost on this question, I was wondering if anyone could help me.

Amy's fave cereal comes in 2 sizes. Small box is 750 grams and costs $3.99, big box is 2.5 kg and costs $12.49. How much does Amy save by buying the giant box?


Would I set this up as a ratio, 750/2500 = 3.99/12.49? Where would I go from there? If someone could please help me that would be great. Thanks so much.

 

[tkhunny]

One way -- Calculate unit prices.

3.99 / 0.75 vs 12.49/2.5

Another way -- Use ½ kg as the base unit

(2500/750)*3.99 vs 12.49

 

[mathguy]

One way -- Calculate unit prices.

3.99 / 0.75 vs 12.49/2.5

Another way -- Use ½ kg as the base unit

(2500/750)*3.99 vs 12.49

OK thanks I've done that. 3.99/0.75 is 5.32 and 4.996. I don't understand how to use this info, what does it show? How would I see how much she would save by buying the giant box? Would I take away 5.32-4.996? I'm really confused. Sorry, math isn't my strong point although I do the questions

 

[tkhunny]

If you buy 1 kg - the unit of measure,

----- It costs $5.32 if you buy this amount in small boxes (ignore for a moment that it requires 1 + (1/3) boxes to do that)
----- It costs $4.996 if you buy this amount in large boxes (ignore for a moment that it requires 2/5 boxes to do that)
----- Savings for 1 kg = 5.32 - 4.996 = 0.324 -- Savings is 32¢ / kg

Buy 10 kg and the savings is $3.20
Buy 100 kg and the savings is $32.00

It is an odd question. One doesn't necessarily save anything by buying the large box, since the large box is not an integer multiple of the small box. One loses money if one only needs the small box. There are various considerations.

I would answer in terms of a standard unit, 32¢ / kg.

 

[mathguy]

That makes perfect sense to me, the answer key though says 18 cents.

They divide 750 by 3 and $3.99 by 3, then multiply the answer (250, $1.33) by 10. Then they subtract $13.30 - $12.49 and get 81 cents. I don't understand why though. What do you think?

 

[Denis]

Lookit MG, you need to STOP complicating things :shock:

750kg = 3.99 ; then 1kg = 3.99 / 750 = .00532
At that price, 2500kg = 2500 * .00532 = 13.30
13.30 - 12.49 = .81

 

[JeffM]

That makes perfect sense to me, the answer key though says 18 cents.

They divide 750 by 3 and $3.99 by 3, then multiply the answer (250, $1.33) by 10. Then they subtract $13.30 - $12.49 and get 81 cents. I don't understand why though. What do you think?

The fundamental point is, as, tkhunny has already mentioned, is that this is not a particularly well specified question.

Implicitly they are asking the question, "How much does Amy save by buying 1 large package rather than 3 small packages?" This is a REALLY stupid question because 3 small packages contain 2.25 kg so the two quantities practicably purchasable are not the same.

The book's answer is certainly confusing as well.

Let's calculate the price per kilogram for both boxes.
Big box: $12.49 / 2.5kg = $4.996/kg.
Sml box: $3.99 / 0.75kg = $5.32/kg.

The difference is $0.324/kg.

So, 2.5kg * $0.324/kg = $0.81.