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Ken has a group of coins worth $6.70. He has four times as many nickels as dimes, and twenty fewer quarters than nickels. How many quarters does he have? A) 19 B) 18 C) 16 D) 15 E) 14 _________________ Why do we fall?...So we can learn to pick ourselves up again If you like the post, give it a KUDOS! CEO  V Joined: 12 Sep 2015 Posts: 3528 Location: Canada Re: Ken has a group of coins worth$6.70. He has four times as many nickel  [#permalink]

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Abhi077 wrote:
Ken has a group of coins worth $6.70. He has four times as many nickels as dimes, and twenty fewer quarters than nickels. How many quarters does he have? A)19 B)18 C)16 D)15 E)14 Let x = the NUMBER of dimes So, 4x = the NUMBER of nickels And 4x - 20 = the NUMBER of quarters One dime is worth$0.1, so 0.10x = the total VALUE of the dimes (in dollars)
Likewise, (0.05)(4x) = the total VALUE of the nickels (in dollars)
And (0.25)(4x - 20) = the total VALUE of the quarters (in dollars)

The total VALUE of all coins is $6.70 So, we can write: 0.10x + (0.05)(4x) + (0.25)(4x - 20) = 6.70 Simplify to get: 0.10x + 0.20x + x - 5 = 6.70 Simplify again to get: 1.3x - 5 = 6.70 Add 5 to both sides to get: 1.3x = 11.70 Solve: x = 11.70/1.3 = 9 So, there are 9 DIMES, 36 nickels and 16 quarters. Answer: C Cheers, Brent _________________ Director  G Joined: 19 Oct 2013 Posts: 508 Location: Kuwait GPA: 3.2 WE: Engineering (Real Estate) Re: Ken has a group of coins worth$6.70. He has four times as many nickel  [#permalink]

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Abhi077 wrote:
Ken has a group of coins worth $6.70. He has four times as many nickels as dimes, and twenty fewer quarters than nickels. How many quarters does he have? A)19 B)18 C)16 D)15 E)14 Let x be the number of nickels, Y be the number of dimes, and Z be the number of quarters Four times as many nickels as dimes can be translated into (1) x = 4y (1) z = x - 20 (2) which can be rearranged to be z + 20 = x 6.70 = 0.05x+0.1y+0.25z 6.70 = 0.05*4y+0.1y+0.25(4y-20) 6.70 = 0.2y+0.1y+1y - 5 11.70 = 1.3y Y = 9 X = 36 Z = 36 - 20 = 16 << number of quarters. Another approach would be to pick a number after setting up the initial equations (1) and (2) If we select Z = 16 then x would be 36 If we multiply 16 * 0.25 = 4 And 36 * 0.05 = 1.8 X = 36 then y is 9 9*0.1 = 0.9 1.8+0.9+4 = 6.70. Answer choice C Posted from my mobile device GMATH Teacher P Status: GMATH founder Joined: 12 Oct 2010 Posts: 918 Re: Ken has a group of coins worth$6.70. He has four times as many nickel  [#permalink]

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Ken has a group of coins - nickels, dimes and quarters only - worth $6.70. He has four times as many nickels as dimes, and twenty fewer quarters than nickels. How many quarters does he have? A)19 B)18 C)16 D)15 E)14 Let N be the number of nickels, D the number of dimes, Q the number of quarters and let us consider CENTS as the "problem´s unit". Doing so, we have: $$N = 4D\,\,\,\,\, \Rightarrow \,\,\,\,5N = 20D$$ $$Q = N - 20\,\,\,$$ $$? = Q = N - 20$$ $$5N + 10D + 25Q = 670\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,2} \,\,\,10N + 5N + 50\left( {N - 20} \right) = 2 \cdot 670$$ $$65N = 2 \cdot 670 + 1000\, = 20\left( {67 + 50} \right)\,\,\,\,\mathop \Rightarrow \limits^{:\,\,5\,\,} \,\,\,\,13N = 4\left( {9 \cdot 13} \right)\,\,\,\,\,\, \Rightarrow \,\,\,N = 36$$ $$? = 16\,\,$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net Target Test Prep Representative P Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 5454 Location: United States (CA) Re: Ken has a group of coins worth$6.70. He has four times as many nickel  [#permalink]

Abhi077 wrote:
Ken has a group of coins worth $6.70. He has four times as many nickels as dimes, and twenty fewer quarters than nickels. How many quarters does he have? A) 19 B) 18 C) 16 D) 15 E) 14 Let’s let Q = the number of quarters, D = the number of dimes, and N = the number of nickels that Ken has. We can create the money value equation as: 0.25Q + 0.1D + 0.05N = 6.7 25Q + 10D + 5N = 670 5Q + 2D + N = 134 We also know that Ken has has four times as many nickels as dimes, and twenty fewer quarters than nickels. We can create two additional equations, as follows: N = 4D N/4 = D and N - 20 = Q Substituting into the money value equation, we have: 5(N - 20) + 2(N/4) + N = 134 5N - 100 + N/2 + N = 134 6N + N/2 = 234 Multiplying by 2, we have: 12N + N = 468 13N = 468 N = 36, so he has 16 quarters Alternate Solution: We know that N = 4D and N - 20 = Q We see that N is a multiple of 4 and since 20 is also a multiple of 4, Q must be a multiple of 4 also. Looking at our answer choices, only choice C is a multiple of 4, so C must be the correct choice. Answer: C _________________ # Scott Woodbury-Stewart Founder and CEO Scott@TargetTestPrep.com See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews Re: Ken has a group of coins worth$6.70. He has four times as many nickel   [#permalink] 07 Oct 2018, 19:36
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# Ken has a group of coins worth \$6.70. He has four times as many nickel

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