The regular price of a coffee at a certain coffee shop is $4

Question

The regular price of a coffee at a certain coffee shop is $4, but every coffee a customer orders beyond the number the customer ordered the previous month is discounted by 20%. Last February, Massie ordered 50 coffees and paid an average of $3.84 per coffee. If she paid an average of $3.70 per coffee for the coffees she ordered last March, how many coffees did she order during the first three months of last year?

(A) 150
(B) 154
(C) 165
(D) 170
(E) 180

Show Answer

Official Answer

D

(A) 150
(B) 154
(C) 165
(D) 170
(E) 180

paragw · Answer

For  Feb :
Use alligation
4.00.............3.20
..........3.84
0.64.............0.16
It gives us ratio of coffees purchased @ $4 and coffees purchased @ $3.2 i.e. 4:1
 Total 50 coffees were ordered in Feb. 
Therefore, coffees purchased @ $4 are 40 & coffees purchased @ $3.2 are 10
This implies that 10 more coffees were purchased in Feb than from Jan
 Therefore, number of coffees purchased in Jan were 40

Now for  March :
Use alligation
4.00.............3.20
..........3.70
0.50.............0.30
It gives us ratio of coffees purchased @ $4 and coffees purchased @ $3.2 i.e. 5:3
Total 50 coffees were ordered in Feb. Therefore, coffees purchased @ $4 are 50 & coffees purchased @ $3.2 are 30
 Total coffees purchased in March are 50+30 = 80

Hence, total coffees ordered during the first three months of last year = 40+50+80 =  170

ankushsambare · Answer

Great question.
Today  kevincan  woke up and chose violence.

MartyMurray · Answer

The regular price of a coffee at a certain coffee shop is $4, but every coffee a customer orders beyond the number the customer ordered the previous month is discounted by 20%. Last February, Massie ordered 50 coffees and paid an average of $3.84 per coffee. If she paid an average of $3.70 per coffee for the coffees she ordered last March, how many coffees did she order during the first three months of last year?

We can start by seeing that the discounted price is 4 × (1 - 0.20) = 4 × 0.80 = 3.20.

Using that information and using alligation, we can determine the following for February:

3.20 <----64----> 3.84 <-16-> 4.00

Ratio of $3.20 coffees : $4.00 coffees = 16 : 64 = 1 : 4 = 10 : 40

We can use that information to determine that she bought 40 in January since the number she paid full price for in February would match the January number.

Now, let's do March.

3.20 <---50---> 3.70 <--30--> 4.00

Ratio of 3.20 coffees : 4.00 coffees = 30 : 50

So, in March, she bought 50 at full price to match February and another 30 a the discounted price.

So, the March total was 80.

Total = 40 + 50 + 80 = 170

(A) 150
(B) 154
(C) 165
(D) 170
(E) 180

Correct answer: D

The regular price of a coffee at a certain coffee shop is $4

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The regular price of a coffee at a certain coffee shop is $4

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