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# A grocer has 400 pounds of coffee in stock, 20 percent

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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink]
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kanusha wrote:
1 , 20% of 400 mean 320 , Next 60% of 100 mean 40 … so on total 360 is the coffee Out of total 500 pounds of coffee. 500 is 100% , 360 pounds = ?%..... 3600/500 = 72% is Original it mean 28%is Decaffeinated. So A

2, Using multipliers… 20% mean 0.2 60% mean 0.6 …. So multiplying both the multipliers 0.12 ??

Can anyone solve this using multipliers as approach?

Kanusha, never mix percents if you take them from different numbers!

In this case decaffeinated coffee= 0.2*400+0.6*100=140. So, again 140/500*100%=28%.
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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink]
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kanusha wrote:
A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?

A. 28%
B. 30%
C. 32%
D. 34%
E. 40%

Since the grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated, 0.2 x 400 = 80 pounds are decaffeinated.

Since the grocer buys another 100 pounds of coffee, 60 percent of which is decaffeinated, the grocer has 60 more pounds of decaffeinated coffee.

Thus, the percentage of decaffeinated coffee is (80 + 60)/(400 + 100) = 140/500 = 28/100 = 28%.

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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink]
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This can be thought of in terms of weighted averages.

the initial coffee is 400 pounds and the latter coffee is 100 pounds so the first gets a weight of 4/5 and the latter gets a weight of 1/5.

20(4/5)+60(1/5)=

16+12=

28
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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink]
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Alternate method: Alligation method

400 pounds (20%) 100 Pounds (60%) {qty 4:1}

{Difference in ratio is 60-20=40% ==> Concentration will be in reverse ratio ==> 1:4 ==> 1/5*40=8 or 4/5*40=32}

Answer : 20+8 or 60-32 = 28%
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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink]
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20% of 400 is decaf

20% * 400 = 80

60% of 100 is decaf

60% * 100 = 60

(80 + 60) = 140

Total pounds of coffee = 400 + 100 = 500

$$\frac{140}{500}$$ (multiply both by 2 to make easier to deal with as a percentage) = $$\frac{28}{100}$$ = 28%

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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink]
20% of 400 is decaffeinated

20% * 400 = 80

60% of 100 is decaffeinated

60% * 100 = 60

(80 + 60) = 140

Total pounds of coffee = 400 + 100 = 500

500 * decaffeinated / 100 = 140
5 * decaffeinated = 140
decaffeinated = 28 %

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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink]
kanusha wrote:
A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?

A. 28%
B. 30%
C. 32%
D. 34%
E. 40%

How can I apply the concentration method here? I tried but fails. I hope you can help please.

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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink]
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kanusha wrote:
A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?

A. 28%
B. 30%
C. 32%
D. 34%
E. 40%

It is a weighted average problem.

Concentration of decaf in original inventory = 20%
Concentration of decaf in new inventory = 60%

Concentration of decaf in mix = ?

w1/w2 = (A2 - Aavg)/(Aavg - A1)

400/100 = (60 - Aavg)/(Aavg - 20)

4*Aavg - 80 = 60 - Aavg

Aavg = 28%

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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink]
kanusha wrote:
A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?

A. 28%
B. 30%
C. 32%
D. 34%
E. 40%

It is a weighted average problem.

Concentration of decaf in original inventory = 20%
Concentration of decaf in new inventory = 60%

Concentration of decaf in mix = ?

w1/w2 = (A2 - Aavg)/(Aavg - A1)

400/100 = (60 - Aavg)/(Aavg - 20)

4*Aavg - 80 = 60 - Aavg

Aavg = 28%

Thanks VeritasKarishma for your keen reply and response. But can I apply the following formula for the problem at hand:

c1 * v1 = c2 * v2

Thanks
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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink]
400/100 = (60 - X)/(X-20) => 4X - 80 = 60 - X; X = 28%
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A grocer has 400 pounds of coffee in stock, 20 percent [#permalink]
kanusha wrote:
A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?

A. 28%
B. 30%
C. 32%
D. 34%
E. 40%

Here is a one line solution using weighted average concept:

Average % (decaffeinated) = (400/500)*20% + (100/500)*60% ---------(where 400/500 = wt. of 1st coffee-type, 100/500 = wt. of 2nd coffee-type)
= (4/5)*20% + (1/5)*60%
= 16% + 12%
= 28%
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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink]
Explanation

= $$0.2(400)+0.6(100) = 140$$ pounds of decaffeinated out of total 500 pounds, which is (140/500)100 = 28%

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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink]
20% of 400 = 80
60% of 100 = 60
total = 500
defac = 140
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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink]
Total Coffee 400 pounds.

Of the total coffee, 20% is decaffeinated, that is (20/100) x 400 = 80 pounds = Quantity of decaffeinated coffee.

Additionally, 100 pounds of coffee are purchased, of which 60% is decaffeinated, that is:

(60/100) x 100 = 60 pounds of decaf.

Percentage of decaffeinated coffee by weight of total coffee = (Decaffeinated coffee / total coffee) x 100
((60 + 80)/500)x100
140/5
28%

An interesting question would be, considering the same statement, what is the percentage of non-decaffeinated coffee by weight of decaffeinated coffee?

Come on you can do it!
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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink]
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Re: A grocer has 400 pounds of coffee in stock, 20 percent [#permalink]
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