Problem Solving

At a certain bakery, the chocolate chip cookies are sold only in packets of three while the peanut butter cookies are sold only in packets of four. If a total of 35 chocolate chip and peanut butter cookies were sold last Tuesday, what is the maximum number of packets of chocolate chip cookies that could have been sold that day.

a. 5

b. 8

c. 9

d. 10

e. 11

points u have to note
1.there are 35 cookies sold(no more no less)
2.in packets of 3 and 4
3.maximum no. of packets

when will maximum no. of packets will occur >> when the least combination of packets is sold more(no. of choc cookies packets is sold more)

choc cookies are sold in packet of 3, now the highest possible no.(< 35) that is divisible by 3 is 33(3*11=33)
for peanut cookies >> 35-33=2
as the peanut cookies are sold in packet of 4(2 is not divisible by 4)
next highest possible no. is 30,that leaves us with 5 for peanut cookies(again not possible,leaves remainder)

next highest possible no. is 27,that leaves us with 8 for peanut cookies(which is 4*2=8,no remainder)

hence 3*[9]=27 and 4*[2]=8
27+8=35

the ans is 9+2=11 [E]

It seems such an easy answer, but at the same time it could be the trick of this problem.
Here we go:
To get max number of chocolate chip cookies, we need to get the smallest number of peanut butter cookies, as follow: 0, 1, 2 etc.
So here 0 could not be, as the question stem states that a certain number of peanut butter cookies were sold, hence it must be either 1 or 2.
If, 1 then the number of chocolate chip cookies would be: 3x+4=35 or 3x=31, hence can not be 1. That leaves us with 2, here we get 3x+2*4=35 or 3x=35-8=27, hence x=9 - max number of packets of chocolate chip cookies that could have been sold (D).
Plese, correct me if I went awry. I want to learn and share, this is the only purpose why I am here:-)

The correct answer is C.

At a certain bakery, the chocolate chip cookies are sold only in packets of three while the peanut butter cookies are sold only in packets of four. If a total of 35 chocolate chip and peanut butter cookies were sold last Tuesday, what is the maximum number of packets of chocolate chip cookies that could have been sold that day.

Let the number of chocolate chip cookie packets be C and
Let the number of peanut butter cookies packets be P

3C + 4P = 35, where P,C are positive integers
3C = 35 - 4P

Different combinations of (C,P) that satisfy the equation are (9,2), (5,5), (1,8).
So 9 is the maximum number of packets of chocolate chip cookies that could have been sold that day

nidhis.1408 wrote:At a certain bakery, the chocolate chip cookies are sold only in packets of three while the peanut butter cookies are sold only in packets of four. If a total of 35 chocolate chip and peanut butter cookies were sold last Tuesday, what is the maximum number of packets of chocolate chip cookies that could have been sold that day.

a. 5

b. 8

c. 9

d. 10

e. 11

We can plug in the answers, which represent the maximum possible number of chocolate-chip cookie packets.
Since we need the MAXIMUM possible value, we should start with the GREATEST answer choice.
When the correct answer choice is plugged in, the remaining number of cookies must be a multiple of 4, since each peanut-butter cookie packet contains 4 cookies.

Answer choice E: 11
Number of chocolate-chip cookies in 11 three-cookie packets = 11*3 = 33.
Remaining number of cookies = 35-33 = 2.
2 is not a multiple of 4.
Eliminate E.

Answer choice D: 10
Number of chocolate-chip cookies in 10 three-cookie packets = 10*3 = 30.
Remaining number of cookies = 35-30 = 5.
5 is not a multiple of 4.
Eliminate D.

Answer choice C: 9
Number of chocolate-chip cookies in 9 three-cookie packets = 9*3 = 27.
Remaining number of cookies = 35-27 = 8.
Success!
The 8 remaining cookies could be contained in 2 packets of peanut-butter cookies, each packet with 4 cookies.

The correct answer is C.