A bakery sold an average(arithmetic mean) of 820 cookies per day in an operating period. On "good" days, the bakery sold

[Vincen]

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?

a) 2:1
b) 3:2
c) 5:4
d) 7:6
e) 9:8

[spoiler]OA=E[/spoiler]

Source: Veritas Prep

[gmatc2020]

Let x = number of "good" day and y = number of "fair" day, we want to know $$\frac{x}{y}$$ or x:y

Given: the bakery sold an average of 820 cookies per day in an operating period

Formula: $$ average\ = \frac{sum\ of\ terms}{number\ of\ terms}$$

Solution:
Setting formula: $$820\ =\ \frac{980\ x\ +\ 640y}{x\ +\ y}$$
Multiple (x + y) on both side: 820x + 820 y = 980x + 640y
Subtract 820x and 640y: 160 x = 180y
Simplify: 8x = 9y
Divide y and 8: $$\frac{x}{y}= \frac{9}{8}$$

Answer: E

[Jay@ManhattanReview]

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?

a) 2:1
b) 3:2
c) 5:4
d) 7:6
e) 9:8

[spoiler]OA=E[/spoiler]

Source: Veritas Prep

Say there were x no. of fair day and y no. of good days.

Thus, 820(x + y) = 980y + 640x

180x = 160y

=> y/x = 180/160 = 9:8

The correct answer: E

Hope this helps!

-Jay
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[Scott@TargetTestPrep]

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?

a) 2:1
b) 3:2
c) 5:4
d) 7:6
e) 9:8

[spoiler]OA=E[/spoiler]

Solution:

We are given that a bakery sold an average (arithmetic mean) of 820 cookies per day in an operating period, and that 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 we let G = the number of good days, and F = the number of fair days, we can create the following equation:

820 = (980G + 640F)/(G + F)

820G + 820F = 980G + 640F

180F = 160G

9F = 8G

G/F = 9/8

Answer: E