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Math Expert V
Joined: 02 Sep 2009
Posts: 56277
Sue and Nancy wish to buy a snack. They combine their money and find t  [#permalink]

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Difficulty:

(N/A)

Question Stats: 83% (02:34) correct 17% (03:00) wrong based on 22 sessions

### HideShow timer Statistics 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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Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3360
Location: India
GPA: 3.12
Sue and Nancy wish to buy a snack. They combine their money and find t  [#permalink]

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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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examPAL Representative P
Joined: 07 Dec 2017
Posts: 1074
Re: Sue and Nancy wish to buy a snack. They combine their money and find t  [#permalink]

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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

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!

_________________ 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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