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# Hadeeqa has 20 coins consisting of quarters and dimes. If she has a to

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Hadeeqa has 20 coins consisting of quarters and dimes. If she has a to [#permalink]

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21 Aug 2017, 11:04
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Difficulty:

25% (medium)

Question Stats:

82% (01:11) correct 18% (01:06) wrong based on 44 sessions

Hadeeqa has 20 coins consisting of quarters and dimes. If she has a total of $3.05, how many dimes does she have? A. 5 B. 7 C. 11 D. 13 E. 17 _________________ Hasan Mahmud SC Moderator Joined: 22 May 2016 Posts: 1759 Hadeeqa has 20 coins consisting of quarters and dimes. If she has a to [#permalink] ### Show Tags 21 Aug 2017, 13:59 Mahmud6 wrote: Hadeeqa has 20 coins consisting of quarters and dimes. If she has a total of$3.05, how many dimes does she have?

A. 5
B. 7
C. 11
D. 13
E. 17

Let x = # of dimes
Let y = # of quarters

x + y = 20
y = 20 - x

.10x + .25y = 3.05

10x + 25y = 305

10(x) + 25(20 - x) = 305

10x + 500 - 25x = 305

195 = 15x

$$\frac{195}{15}$$ = 13 = x

There are 13 dimes.

Check:
13 * .10 = $1.30 7 * .25 =$1.75

$1.30 +$1.75 = $3.05 ------ Alternatively, use answer choices. Example with Answer A. 1) Multiply the number (5) by .10: (5)(.10) = .50 2) Subtract from 3.05 3.05 - .50 = 2.55 3) 2.55 is NOT divisible by .25. Reject and move on Keep going until you find the value which, after subtraction by the dimes' value, lets you divide by .25. That's D, where 1.75/.25 = 7 Then add # dimes + # quarters to be sure you have 20 coins. _________________ In the depths of winter, I finally learned that within me there lay an invincible summer. -- Albert Camus, "Return to Tipasa" Manager Joined: 27 Dec 2016 Posts: 231 Concentration: Marketing, Social Entrepreneurship GPA: 3.65 WE: Marketing (Education) Re: Hadeeqa has 20 coins consisting of quarters and dimes. If she has a to [#permalink] ### Show Tags 22 Aug 2017, 09:51 1 Mahmud6 wrote: Hadeeqa has 20 coins consisting of quarters and dimes. If she has a total of$3.05, how many dimes does she have?

A. 5
B. 7
C. 11
D. 13
E. 17

I use principal from mixture problems.

Let X = quarters and Y = dimes.

$$X + Y = 20$$ ...(equation 1)
$$0.25X + 0.1Y = 3.05$$
multiply both sides with 100 : $$25X + 10Y = 305$$ ...(equation 2)

We want to know how manys dimes (Y), so we change our equation to Y.
- From eq.1 : $$X = 20-Y$$.
- Plug into eq.2 : $$25(20-Y) + 10Y = 305$$ --> $$500 - 25Y + 10Y = 305$$ --> $$-15Y = -195.$$ Y is 13.

D.
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Re: Hadeeqa has 20 coins consisting of quarters and dimes. If she has a to [#permalink]

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22 Aug 2017, 23:42
Mahmud6 wrote:
Hadeeqa has 20 coins consisting of quarters and dimes. If she has a total of $3.05, how many dimes does she have? A. 5 B. 7 C. 11 D. 13 E. 17 lets solve backwards if 17 dimes then 170 + 25*3 = 245 not equal to 305 if 13 dimes then 130 + 25*7 = 130 + 175 = 305 answer D _________________ We must try to achieve the best within us Thanks Luckisnoexcuse Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 2773 Location: United States (CA) Re: Hadeeqa has 20 coins consisting of quarters and dimes. If she has a to [#permalink] ### Show Tags 24 Aug 2017, 16:01 1 Mahmud6 wrote: Hadeeqa has 20 coins consisting of quarters and dimes. If she has a total of$3.05, how many dimes does she have?

A. 5
B. 7
C. 11
D. 13
E. 17

We will create a “number of coins” equation and a “money” equation. Let’s let d = the number of dimes and q = the number of quarters. We create the “number of coins” equation as:

q + d = 20

q = 20 - d

The “money” equation uses the facts that a quarter is 25 cents, a dime is 10 cents, and $3.05 is 305 cents: 25q + 10d = 305 5q + 2d = 61 We substitute (20 - d) for q and get: 5(20 - d) + 2d = 61 100 - 5d + 2d = 61 -3d = -39 d = 13 Answer: D _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Intern Joined: 27 Mar 2018 Posts: 11 Re: Hadeeqa has 20 coins consisting of quarters and dimes. If she has a to [#permalink] ### Show Tags 21 May 2018, 04:35 ScottTargetTestPrep wrote: Mahmud6 wrote: Hadeeqa has 20 coins consisting of quarters and dimes. If she has a total of$3.05, how many dimes does she have?

A. 5
B. 7
C. 11
D. 13
E. 17

We will create a “number of coins” equation and a “money” equation. Let’s let d = the number of dimes and q = the number of quarters. We create the “number of coins” equation as:

q + d = 20

q = 20 - d

The “money” equation uses the facts that a quarter is 25 cents, a dime is 10 cents, and $3.05 is 305 cents: 25q + 10d = 305 5q + 2d = 61 We substitute (20 - d) for q and get: 5(20 - d) + 2d = 61 100 - 5d + 2d = 61 -3d = -39 d = 13 Answer: D Thank you sir I don't know about dime! Factual information about money. Senior Manager Joined: 31 May 2017 Posts: 282 Re: Hadeeqa has 20 coins consisting of quarters and dimes. If she has a to [#permalink] ### Show Tags 21 May 2018, 23:05 Hadeeqa has 20 coins consisting of quarters and dimes. If she has a total of$3.05, how many dimes does she have?

The total value $3.05 ends with a 5. So the number of quarters should be 5 or 7. Anything high or more will exceed the value as well as total 20 coins. Step 1: Maximum number of quarters we can have is 12 (3$) , so in the answer choices, we can eliminate choices 1 , 2.
Step 2: If the number of dimes is 11, then quarters would need to be 9, then sum exceeds $3.05. so we can eliminate choice 3 We can also eliminate option E by the process of elimination, more number of dime means less total value. Option 3 , 13 is the right answer. Ans: D _________________ Please give kudos if it helps Resources | | | | | Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 2773 Location: United States (CA) Re: Hadeeqa has 20 coins consisting of quarters and dimes. If she has a to [#permalink] ### Show Tags 22 May 2018, 17:41 Mahmud6 wrote: Hadeeqa has 20 coins consisting of quarters and dimes. If she has a total of$3.05, how many dimes does she have?

A. 5
B. 7
C. 11
D. 13
E. 17

Letting q = the number of quarters and d = the number of dimes, we can first create the equation for the number of coins:

q + d = 20

q = 20 - d

Since each quarter is worth 25 cents, each dime is worth 10 cents, and \$3.05 = 305 cents, we have:

25q + 10d = 305

5q + 2d = 61

Substituting, we have:

5(20 - d) + 2d = 61

100 - 5d + 2d = 61

3d = 39

d = 13

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Re: Hadeeqa has 20 coins consisting of quarters and dimes. If she has a to   [#permalink] 22 May 2018, 17:41
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