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Re: M0433
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24 Oct 2014, 22:52
Bunuel wrote: Official Solution:
In the office supply store, Brittany bought 17 pens of three kinds: ball pens, gel pens, and ink pens, which cost $0.05, $0.10 and $0.25 each. The total that Brittany paid was $2.05. If Brittany bought twice as many gel pens as ink pens, how many ball pens did she buy?
A. 4 B. 5 C. 7 D. 8 E. 10
Denote each pen with the first letter of its kind and build a system of equations: \(5B+10G+25I=205\) \(B+G+I=17\) \(G=2I\) \(B+9I=41\) \(B+3I=17\) \(6I=24\) \(I=4\) \(B=5\)
Answer: B Hi Bunuel, Thanks for your explanation. Can you please clarify how you received the equation B +9I = 41? I understand how you received B +3I =17. Thanks a lot! Aram



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Re: M0433
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25 Oct 2014, 05:38
safaria25 wrote: Bunuel wrote: Official Solution:
In the office supply store, Brittany bought 17 pens of three kinds: ball pens, gel pens, and ink pens, which cost $0.05, $0.10 and $0.25 each. The total that Brittany paid was $2.05. If Brittany bought twice as many gel pens as ink pens, how many ball pens did she buy?
A. 4 B. 5 C. 7 D. 8 E. 10
Denote each pen with the first letter of its kind and build a system of equations: \(5B+10G+25I=205\) \(B+G+I=17\) \(G=2I\) \(B+9I=41\) \(B+3I=17\) \(6I=24\) \(I=4\) \(B=5\)
Answer: B Hi Bunuel, Thanks for your explanation. Can you please clarify how you received the equation B +9I = 41? I understand how you received B +3I =17. Thanks a lot! Aram From \(5B+10G+25I=205\) and \(G=2I\) we get \(5B+10*(2I)+25I=205\) > \(5B+45I=205\) > \(B+9I=41\). Hope it's clear.
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Re: M0433
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04 Nov 2014, 20:12
To solve this we need to set up a system of equations.
Equation 1: B+G+i=17; where B,G, and i, are the number of each type pen purchased, respectively. Equation 2: 5B +10G+25i=205; reduce by dividing each term by 5 > *B+2G+5i=41* (this is the equation we'll use). Equation 3: G=2i
Sub eq.3 into eq.2 > B+2(2i)+5i=41 > *B+9i=41*
We want to end up with a value for B, so isolate i >9i=41B > *i=(41B)/9*
Plug the value of i into eq1: B+G+i=17 > (B)+((822B)/9)+((41B)/9)=17 (The middle term is 2i, or twice the last term).
simplify: (9B/9)+((822B)/9)+((41B)/9)=17
(9B+822B+41B)/9=17
(9B+822B+41B) = 17*9 = 153
6B+123=153
B=5



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Re: M0433
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09 Dec 2014, 07:40
Let, ink pens be x Gel pen = 2x and ball pen = (173x)
Now, 25x+20x+(173x)5 = 205 Solving we get x=4
Therefore ball pen = 173*4 =5



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an approach if you face time constraint: 1. b + g + i = 17 2. b + 2i + i= 17 (obviously g/i=2/1) 3. given the above only answer B and D suffice (the rest options do not result into integer values), i.e. B. 5 + 3*4 = 17 (where g/i=8/4) orD. 8 + 3*3 = 17 (g/i=6/3) 4. from here you can play the game choose either after 30 secs or solve further using the given info re prices and spend additional 15 secs. D. 8*$5 + 6*$10 + 3*$25 > does not equal $205, hence wrong, ANSWER B should be correct. We are done.Just to check: B: 5*$5 + 8*$10 + 4*$25=$205. correct
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Re M0433
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11 Sep 2016, 01:08
I think this is a highquality question and I agree with explanation.



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Re: M0433
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31 Aug 2018, 11:42
Lets Say, Ball PEN BP, Gel PEN GPInk PEN IPGiven : GP= 2IP (Brittany bought twice as many gel pens as ink pens) BP + GP + IP = 17Alternative Approach: BP + GP + IP = 17 BP + 2IP + IP =17 (using GP= 2 x IP ) BP + 3IP = 17IP must be a integer. That makes 3IP , a multiple of 3. chk for values of IP=1,2,3,4,5.... Use GP= 2IP as limiting condition to chk BP + GP + IP = 17. The values that makes sense are 5 & 8 (Among options given) Put the cost values & check. Answer: 5










