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# A bag of coins contains only nickels, dimes, and quarters. There are 3

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Math Expert
Joined: 02 Sep 2009
Posts: 55801
A bag of coins contains only nickels, dimes, and quarters. There are 3  [#permalink]

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20 Dec 2018, 02:20
00:00

Difficulty:

35% (medium)

Question Stats:

71% (01:40) correct 29% (02:05) wrong based on 91 sessions

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A bag of coins contains only nickels, dimes, and quarters. There are 38 coins in all. What is the total value of all the coins in the bag? (Quarter = 25 cents; dime = 10 cents;
nickel = 5 cents)

(1) Quarters account for half the value of the coins in the bag.

(2) The value of all the dimes equals the value of all the nickels.

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Joined: 22 Sep 2018
Posts: 249
Re: A bag of coins contains only nickels, dimes, and quarters. There are 3  [#permalink]

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25 Dec 2018, 19:42
Bunuel wrote:
A bag of coins contains only nickels, dimes, and quarters. There are 38 coins in all. What is the total value of all the coins in the bag? (Quarter = 25 cents; dime = 10 cents;
nickel = 5 cents)

(1) Quarters account for half the value of the coins in the bag.

(2) The value of all the dimes equals the value of all the nickels.

Let's set our variables:

Nickels = x
Dimes = y
Quarters = z

Total coins -> x + y + z = 38

Prompt: What is the total value of coins in the bag? translated -> 5x + 10y + 25z = ??

Statement 1:
25z = 5x + 10y
x + y + z = 38

3 variables, 2 equations. No eliminations possible, thus INSUFF

Statement 2:
10y = 5x
x + y + z = 38

Once again 3 variables, 2 equations. No eliminations possible, thus INSUFF

Combined, we have enough information to solve for each variable.

Re: A bag of coins contains only nickels, dimes, and quarters. There are 3   [#permalink] 25 Dec 2018, 19:42
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