A caterer is preparing a cookie platter with oatmeal, chocolate chip,

Question

A caterer is preparing a cookie platter with oatmeal, chocolate chip, and peanut butter cookies. The customer wants twice as many oatmeal cookies as chocolate chip cookies and cannot spend more than $30.00 for the entire platter. If oatmeal cookies cost 25 cents each, chocolate chip cookies are 75 cents each and peanut butter cookies are 50 cents each, and the total number of cookies is 50, how many chocolate chip cookies can be included in the platter without exceeding the $30.00 price limit?

A. 7
B. 8
C. 14
D. 16
E. 28

A. 7
B. 8
C. 14
D. 16
E. 28

yashikaaggarwal · Answer

25?+75?+50? < 3000
?+3?+2? < 120
?+?+? = 50
????, ? = 2?

??? ??? ??. ?? ????????? ?????? = 
A. 7 = ?
14 = ?
??? ? = 50-7-14 = 29
14+7(3) +2(29) < 120
14+21+58 < 120
93<120 (?? ???? ?? ??? ??????? ???? ????????? ?????? ????) (?????????)

B. 8 = ?
16 = ?
??? ? = 50-8-16 = 26
16+8(3) +2(26) < 120
16+24+52 < 120
92<120 (?? ???? ?? ??? ??????? ???? ????????? ?????? ????) (?????????)

C. 14 = ? 
28 = ?
??? ? = 50-14-28 = 8
28+14(3)+2(8) < 120
28+42+16 < 120
86<120 (?? ???? ?? ??? ??????? ???? ????????? ?????? ????) (?????????)

D. 16 = ? 
32 = ?
??? ? = 50-16-32 =2
32+16(3)+2(8) < 120
28+42+16 < 120
86<120

E. 28 = ? 
56 = ?
??? ? = 50-56-28 = -34
??????? ???'? ?? ?? ????????.(?????????)

????????? ?? ??? ???? ?? ??? 16 ????????? ??????? ??????? ????????? ??? ????? ???????????.

??? ?

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Lipun · Answer

O + C + P = 50 and O = 2C
=> 3C + P = 50

max C = 16

check if the total price is less than 3000 cents

25*O + 50*C + 75*P = 2*50*C + 75*P = 100*16 + 75*2 = 1600 + 150 = 1750 (<3000)

Ans: D

stne · Answer

Question says  cannot  spend more than $30 hence customer  can  spend $30.

Let Chocolate chip be  x  then oat meal  2x  and Butter cookies  y

So we have  2x+x+y=50  
 2x(25)+x(75)+y(50)= 3000

After simplification:

3x+y=50  (i)
 125x+50y=3000  (ii)

Solving (i) and (ii) we get  x=20   hence customer can purchase a max. of 20 Chocolate chip cookies with $30 within the given constraints.

However since 20 is not among the options hence the next max. number of Chocolate cookies among the options is 16.

Hence D.

Hope it's helps.

catinabox · Answer

Can you check your solution once? If x=20, i.e chocolate chip cookies = 20, then oatmeal cookies = 2x=40. 40+20=60> 50, so the solution is not possible.

ScottTargetTestPrep · Answer

Solution: 
 
The question has been misstated; it should read that we want the  maximum  number of chocolate chip cookies that would fulfill the constraints. (Otherwise, choices A, B, C, and D would all be correct. We leave it to the reader to verify.)

Without doing a lot of algebra, let’s consider the answer choices. Since we are looking for the maximum number of chocolate chip cookies, let’s start with choice E. We see it is an impossible answer because, if there were 28 chocolate chip cookies, we would need twice that number (56) of oatmeal cookies, and the sum of 84 cookies exceeds the 50-cookie limit.

Consider Choice D. If we have 16 chocolate chip cookies, then we have twice that number (32) oatmeal cookies. This allows for 2 peanut butter cookies. The total cost is 16*0.75 + 32*0.25 + 2*0.50 = $21.00, which is less than the $30 limit for the platter.

We need go no further. Choice D is correct.

Answer: D

A caterer is preparing a cookie platter with oatmeal, chocolate chip,

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A caterer is preparing a cookie platter with oatmeal, chocolate chip,

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