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505-555 Level|   Algebra|                           
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A collection of 16 coins, each with a face value of either 10 cents or 02 May 2021, 22:07
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AbdurRakib
A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35. How many of the coins have a face value of 25 cents?

A) 3
B) 5
C) 7
D) 9
E) 11



Answer: Option B

Video solution by GMATinsight

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A collection of 16 coins, each with a face value of either 10 cents or 04 Sep 2021, 09:12
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Correct option : B - Answer 5

10 cents and 25 cents = 235 cents
10x+25y = 235.................(i)

10 cents and 25 cents total 16 coins
x+y = 16 .................(ii)
Multiply by 10
10x+10Y = 160 ............(iii)

Eliminate x
15 y = 75
25 cents =5
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A collection of 16 coins, each with a face value of either 10 cents or 12 Jun 2022, 13:40
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AbdurRakib
A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35. How many of the coins have a face value of 25 cents?

A) 3
B) 5
C) 7
D) 9
E) 11

Another approach is to use algebra:

Let Q = # of quarters ($0.25)
So, 16 - Q = # of dimes ($0.10)

We're told that: (value of quarters) + (value of dimes) = $2.35
So, we get: 0.25Q + 0.10(16 - Q) = 2.35
Expand: 0.25Q + 1.6 - 0.1Q = 2.35
Simplify: 0.15Q + 1.6 = 2.35
0.15Q = 0.75
Q = 5

Answer:
Show Spoiler
B

Here are some videos that cover the concepts required to answer this question:



BrentGMATPrepNow
Thank you for this explanation. Can you use a combo to solve this problem?

I did 0.1x+.25y=2.35
+ x+y=16
----------------------------------
--> I multiplied the top equation by 100 to get 1-x+25y=235 and the bottom equation by -10 to cancel out the x's to get --> y=5
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A collection of 16 coins, each with a face value of either 10 cents or 12 Jun 2022, 13:55
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woohoo921
Thank you for this explanation. Can you use a combo to solve this problem?

I did 0.1x+.25y=2.35
+ x+y=16
----------------------------------
--> I multiplied the top equation by 100 to get 1-x+25y=235 and the bottom equation by -10 to cancel out the x's to get --> y=5

Your calculations are perfect.
For questions of this nature, we can often use one variable to solve the question or two variables.
Typically, one variable will be faster, but not so much faster that you shouldn't use two variables.
Either works.
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A collection of 16 coins, each with a face value of either 10 cents or 12 Jun 2022, 21:06
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AbdurRakib
A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35. How many of the coins have a face value of 25 cents?

A) 3
B) 5
C) 7
D) 9
E) 11

As always, if the instinct is to start setting up an algebraic equation, I'd at least consider using PITA (Plug In The Answers). I like testing B and D. B looks easy to work with, so let's start there.
5 25-cent coins and 11 10-cent coins.
5*$0.25 = $1.25
11*$0.10 = $1.10
That's a total of $2.35.
Answer choice B.

If that hadn't worked, we'd have known whether we need a higher value or a lower value. If lower, A would have been right. If higher, we only would have to test D. If D were too high, C is would be the only thing between B and D. If D were too low, we'd know we needed something even higher, so E would be the only option.


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A collection of 16 coins, each with a face value of either 10 cents or 16 Jun 2022, 21:48
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There are two ways to solve questions with systems of two equation non proportional and two variables: substitution or elimination.
This in particular was solved by elimination.
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A collection of 16 coins, each with a face value of either 10 cents or 31 May 2023, 04:33
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AbdurRakib
A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35. How many of the coins have a face value of 25 cents?

A) 3
B) 5
C) 7
D) 9
E) 11
We know that number of $0.25 + number of $0.10= 16 and the face value is $2.35
Start with option C [to find whether I should try larger or smaller numbers]
Option C: 7*$0.25= $1.75, which means the other 9 coins are 10 cents; 9*$0.10= $0.90. In total, $1.75+$0.90=$2.65. [ Wrong answer but now I know that the number $0.25 will be less than 7] So try option B
Option B: 5*$0.25= $1.25, which means the other 11 coins are 10 cents; 11*$0.10= $1.10. In total, $1.25+$1.10=$2.35. Right answer.
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A collection of 16 coins, each with a face value of either 10 cents or 27 Jun 2025, 09:26
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