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25 Dec 2018, 14:11
3
00:00

Difficulty:

55% (hard)

Question Stats:

63% (03:16) correct 37% (03:00) wrong based on 37 sessions

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A coin bank with nickels, dimes and quarters contains coins worth $35.80. If there are twice as many nickels as there are dimes, and 10 more quarters than dimes, how many nickels are there? (Note - 1 Nickel =5 cents, 1 dime = 10 cents and 1 quarter =25 cents) a. 186 b. 148 c. 96 d. 55 e. 48 Math Expert Joined: 02 Aug 2009 Posts: 7757 Re: A coin bank with nickels, dimes and quarters contains coins worth$35.  [#permalink]

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25 Dec 2018, 19:41
Jazzmin wrote:
A coin bank with nickels, dimes and quarters contains coins worth $35.80. If there are twice as many nickels as there are dimes, and 10 more quarters than dimes, how many nickels are there? (Note - 1 Nickel =5 cents, 1 dime = 10 cents and 1 quarter =25 cents) a. 186 b. 148 c. 96 d. 55 e. 48 Let the numbers be nickels n, dime d and quarter q.. So total we have is 35.80$ or 3580 cents..
Now
n=2d,
q=10+d,
5n+10d+25q=3580
Substitute the values of n and q in terms of d in this equation..
5*2d+10d+25(10+d)=3580.......10d+10d+250+25d=3580
45d=3580-250=3330.....
$$d=\frac{3330}{45}=74$$
If d is 74, n is 2*d=2*74=148..
B
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26 Dec 2018, 10:43

Solution

Given:
• A coin bank with nickels, dimes and quarters contains coins worth $35.80 • There are twice as many nickels as there are dimes, and 10 more quarters than dimes • 1 Nickel = 5 cents, 1 dime = 10 cents and 1 quarter = 25 cents To find: • The number of nickels present in the coin bank Approach and Working: As we have both nickels and quarters expressed in terms of dimes, let us assume that the number of dimes is n. • Hence, the number of nickels = 2 x n = 2n • And, the number of quarters = 10 + n The total value worth of all three types of coins = [n x 10 + 2n x 5 + (10 + n) x 25] cents = (10n + 10n + 25n + 250) cents = (45n + 250) cents Therefore, we can write • 45n + 250 = 3580 Or, 45n = 3580 – 250 Or, 45n = 3330 Or, n = 74 Therefore, the number of nickels = 74 x 2 = 148 Hence, the correct answer is option B. Answer: B _________________ Re: A coin bank with nickels, dimes and quarters contains coins worth$35.   [#permalink] 26 Dec 2018, 10:43
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