A bakery sold an average (arithmetic mean) of 820 cookies per day in

Question

A bakery sold an average (arithmetic mean) of 820 cookies per day in an operating period. On "good" days, the bakery sold an average of 980 cookies per day, and on "fair" days, the bakery sold an average of 640 cookies per day. If every day in the operating period was either "good" or "fair", what was the ratio of the number of "good" days to the number of "fair" days for the bakery's operating period?

Let's assume, the number of good days are G and the number of fair days are F.
So, 980G+640F=820(G+F)
980G+640F=820G+820F
980G-820G=820F-640F
160G=180F
8G=9F
G:F=9:8

Answer: E.

A. 2:1
B. 3:2
C. 5:4
D. 7:6
E. 9:8

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tgsankar10 · Answer

Total Average sales,  t-820

Average sales on Good days,  g-980

Average sales on Fair days,  f-640

Ratio of Good to Fair days,  \frac{G}{F}=\frac{t-f}{g-t}=\frac{820-640}{980-820}=\frac{180}{160}=\frac{9}{8}

G:F=9:8

Answer: E

Abdelaali91 · Answer

gc=number of cookies in good days
ng=number of good days
fc=number of cookies in fair days
nf=number of fair days

we're looikg for ng:nf or ng/nf let's pose x=ng/nf

(gc+fc)/(ng+nf)=820 (1)

we know gc/ng=980 so gc=980*ng 
we know fc/nf=640 so fc=640*nf

plug in (1) : (980x+640)/(x+1) = 820
so 160x=180 ie x=180/160 so x=9/8
Answer E

satish_sahoo · Answer

2 methods:

1. Algebra- using variable equation-

Let "g" is the number of good days, "f" number of bad days.
As per question:

\(\frac{(980g + 640f)}{g+f} = 820\)
\(980g-820g = 820f-640f\)
\(160g = 180f\)
\(\frac{g}{f} = \frac{180}{160} = \frac{9}{8}\)

hence, \(g:f = 9:8\)

2. weighted averages (preferred method)

\(\frac{g}{f} = \frac{(820-640)}{(980-820)} = \frac{9}{8}\)

hence, \(g:f = 9:8\)

To grasp the concept of weighted averages and the scale method please read through this- https://gmatclub.com/forum/weighted-ave ... 06999.html

Answer opt- E

Hope it helps

prantorboni · Answer

A bakery sold an average (arithmetic mean) of 820 cookies per day in an operating period. On "good" days, the bakery sold an average of 980 cookies per day, and on "fair" days, the bakery sold an average of 640 cookies per day. If every day in the operating period was either "good" or "fair", what was the ratio of the number of "good" days to the number of "fair" days for the bakery's operating period?

Let's assume, the number of good days are G and the number of fair days are F.
So, 980G+640F=820(G+F)
980G+640F=820G+820F
980G-820G=820F-640F
160G=180F
8G=9F
G:F=9:8

Answer: E.

Let's assume, the number of good days are G and the number of fair days are F. 
 So, 980G+640F=820(G+F) 
 980G+640F=820G+820F 
 980G-820G=820F-640F 
 160G=180F 
 8G=9F 
 G:F=9:8

Answer: E.

e3thekid · Answer

We can set this up as a weight average question. Let’s assign g to the number of “good” days and f to the number of “fair” days.

Given the averages for both types of days and the overall average on an operating day, we can set up our equation as:

(Good Day Avg.)(# of Good days) + (Fair day Avg.)(number of fair days) / # of Good and Fair days = Operating Day Avg.

980g + 640f / g + f = 820

980g + 640f = 820g + 820f

160g = 180f

g : f = 180/160 which reduces to 9/8

Option E

A bakery sold an average (arithmetic mean) of 820 cookies per day in

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A bakery sold an average (arithmetic mean) of 820 cookies per day in

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