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Sue and Nancy wish to buy a snack. They combine their money and find t

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Sue and Nancy wish to buy a snack. They combine their money and find t  [#permalink]

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New post 05 Mar 2018, 00:18
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A
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C
D
E

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Question Stats:

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Sue and Nancy wish to buy a snack. They combine their money and find they have $4.00, consisting of quarters, dimes, and nickels. If they have 35 coins and the number of quarters is half the number of nickels, how many quarters do they have? (quarter = $0.25, dime = $0.1, nickel = $0.05)

(A) 3

(B) 5

(C) 6

(D) 10

(E) 20

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Sue and Nancy wish to buy a snack. They combine their money and find t  [#permalink]

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New post 05 Mar 2018, 00:49
Bunuel wrote:
Sue and Nancy wish to buy a snack. They combine their money and find they have $4.00, consisting of quarters, dimes, and nickels. If they have 35 coins and the number of quarters is half the number of nickels, how many quarters do they have? (quarter = $0.25, dime = $0.1, nickel = $0.05)

(A) 3

(B) 5

(C) 6

(D) 10

(E) 20


Let the number of dimes be D, number of quarters be Q, and number of nickles be N

Given data:
\(Q = \frac{N}{2}\)

\(Q + N + D = 35\) -> \(\frac{N}{2} + N + D = 35\) -> \(\frac{3N}{2} + D = 35\) -> \(3N + 2D = 70\) -> (1)

Similarly, \(0.25Q + 0.1D + 0.05N = 4\) -> \(5Q + 2D + N = 80\)(divinding by 0.05)

Substituting the value of Q, we get \(\frac{5N}{2} + N + 2D = 80\) -> \(\frac{7N}{2} + 2D = 80\) -> \(7N + 4D = 160\) -> (2)


Multiplying equation (1) by 2 and subtracting from (2), we get N = 20

Therefore, the number of quarters is \(\frac{N}{2}\) = 10 (Option D)
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Re: Sue and Nancy wish to buy a snack. They combine their money and find t  [#permalink]

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New post 05 Mar 2018, 02:24
Bunuel wrote:
Sue and Nancy wish to buy a snack. They combine their money and find they have $4.00, consisting of quarters, dimes, and nickels. If they have 35 coins and the number of quarters is half the number of nickels, how many quarters do they have? (quarter = $0.25, dime = $0.1, nickel = $0.05)

(A) 3

(B) 5

(C) 6

(D) 10

(E) 20


Instead of creating equations, we'll just use the answers.
This is an Alternative approach.

Say the median, (C), is correct.
Then they have
6 quarters = $1.5
12 nickels = $0.6
35 - 12 - 6 = 17 dimes = $1.70
This sums to $3.8 which is not enough!

Since we need more money, let's take more quarters:
10 quarters = $2.5
20 nickels = $1
35 - 10 - 20 = 5 dimes = $0.5
This sums to $4 - exactly what we need!

(D) is our answer.
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Re: Sue and Nancy wish to buy a snack. They combine their money and find t   [#permalink] 05 Mar 2018, 02:24
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