If each item on your grocery list goes up by 4% then has the total cost

Tuesday Afternoon

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Thu Aug-18-11 07:34 AM
Original message

If each item on your grocery list goes up by 4% then has the total cost

of your groceries only gone up by 4%?

please show the math.

tia.

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Chan790

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Thu Aug-18-11 07:45 AM
Response to Original message

1. In MD, no.

Not much math required.

Some items are untaxed as "food" and other items are taxed as "consumables" (the second one being all prepared foods, soda, and a wide definition of junk food that includes things like sweetened breakfast cereal and frozen pizza and jelly but not "preserves" or peanut butter) so the net change in your grocery bill would depend on the quantities of the items purchased and their taxable status.

For example:

2 pizzas @ $8...16 +tax = $17.60
4 bags of taters @ $4 +tax^0 = $16

Same purchase amounts, different totals because of tax-policy.

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struggle4progress

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Thu Aug-18-11 02:36 PM
Response to Reply #1

8. That shouldn't matter. Suppose there are n classes of grocery items

C1, C2, C3, ... , Cn

taxed at rates r1, r2, r3, ... , rn

and the prices of all items go up p%

The old total would have been

C1*(1 + r1) + C2*(1 + r2) + ... + Cn*(1 + rn)

The new total is

(1 + p/100)*C1*(1 + r1) + (1 + p/100)*C2*(1 + r2) + ... + (1 + p/100)*Cn*(1 + rn)
= (1 + p/100)*(C1*(1 + r1) + C2*(1 + r2) + ... + Cn*(1 + rn))

So the new total is (1 + p/100) times the old total: the total has gone up by p%. It wouldn't matter if some classes Cj were untaxed (rj = 0)

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Chan790

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Thu Aug-18-11 05:37 PM
Response to Reply #8

9. This is going to sound very bad because until recently I advised people on major financial decisions

That was entirely over my head, I have about a 5th grade comprehension of mathematics: arithmetic, pre-algebra and I naturally "get" geometry and trigonometry more than my other math skills would suggest. I fulfilled my college math requirements with accounting courses and a visual-math class meant as an elective for engineers and architects. Also, CAD.

If you can diagram that, I might get it.

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struggle4progress

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Thu Aug-18-11 05:57 PM
Response to Reply #9

10. Use the distributive law:

a*(w + x + y + z + ...) = a*w + a*x + a*y + a*z + ...

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kick-ass-bob

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Thu Aug-18-11 08:37 AM
Response to Original message

2. Yes, outside of taxes.

Edited on Thu Aug-18-11 08:55 AM by kick-ass-bob

5 things in your list at prices: A, B, C, D, E, summed = (price) P

With a 4% increase,
P'(new price)= (A*1.04)+(B*1.04)+(C*1.04)+(D*1.04)+(E*1.04)

factor out the 1.04 from each:
P'=1.04*(A+B+C+D+E)
P'=1.04*P

This is holding all else equal, including your consumption and the package sizes. Adding in taxes changes it, because taxes are rates (and rounded), so the more expensive the total, the more tax you pay. And if you change consumption or package sizes, it throws off the total as well.

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Tuesday Afternoon

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Thu Aug-18-11 08:49 AM
Response to Reply #2

3. How do I factor it out? The cashier just rang it up!

:D :yoiks:

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kick-ass-bob

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Thu Aug-18-11 08:55 AM
Response to Reply #3

4. Well....

how much time do you have? :P

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Tuesday Afternoon

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Thu Aug-18-11 08:58 AM
Response to Reply #4

5. it is just too painful to contemplate. I know it is right but, at the cash

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One_Life_To_Give

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Thu Aug-18-11 11:00 AM
Response to Original message

6. Multiplication Distributive Property

http://www.math.unt.edu/mathlab/emathlab/distributive_property_of_multipl.htm

The distributive property of multiplication over addition is simply this: it makes no difference whether you add two or more terms together first, and then multiply the results by a factor, or whether you multiply each term alone by the factor first, and then add up the results.

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Lionel Mandrake

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Thu Aug-18-11 12:28 PM
Response to Original message

7. The total goes up by approximately 4%.

The approximation is not exact for two reasons:

1. The price of a single item can not go up by exactly 4% unless that price is a multiple of 25 cents.

2. Taxes are rounded to the nearest penny. Thus it's unlikely that the tax will go up by exactly 4%.

Nevertheless, the total cost increase will be close to 4%.

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Philippine expat

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Thu Aug-18-11 09:11 PM
Response to Original message

11. Depends

are groceries taxable in your area, or in states where
groceries are tax exempt do you include things like
detergent, paper towels, etc as groceries. So no because
they will go up the 4% plus extra tax.
Another factor might be that a 4% increase on an item might result
in a fraction of a cent then the price would be either rounded up or down
which would in turn alter your overall percentage

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