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

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Senior Manager
Status: The best is yet to come.....
Joined: 10 Mar 2013
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Kudos [?]: 164 [0], given: 182

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:

35% (medium)

Question Stats:

78% (01:12) correct 22% (01:38) wrong based on 34 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 [Reveal] Spoiler: OA _________________ Hasan Mahmud Kudos [?]: 164 [0], given: 182 Director Joined: 22 May 2016 Posts: 802 Kudos [?]: 254 [0], given: 544 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. Kudos [?]: 254 [0], given: 544 Manager Joined: 27 Dec 2016 Posts: 145 Kudos [?]: 38 [0], given: 192 Concentration: Social Entrepreneurship, Nonprofit GPA: 3.65 WE: Sales (Consumer Products) Re: Hadeeqa has 20 coins consisting of quarters and dimes. If she has a to [#permalink] ### Show Tags 22 Aug 2017, 09:51 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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Joined: 18 Aug 2016
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Kudos [?]: 139 [0], given: 123

GMAT 1: 630 Q47 V29
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 Kudos [?]: 139 [0], given: 123 Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 1634 Kudos [?]: 837 [0], given: 2 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 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

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Kudos [?]: 837 [0], given: 2

Re: Hadeeqa has 20 coins consisting of quarters and dimes. If she has a to   [#permalink] 24 Aug 2017, 16:01
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