A Certain Purse Contains 30 Coins, Each Coin is either a Nickel or GMAT Problem Solving

Question: A certain purse contains 30 coins, Each coin is either a nickel or a quarter. If the total value of all coins in the purse is 4.70$, how many nickels does the purse contain?

1. 12
2. 14
3. 16
4. 20
5. 22

Correct Answer: (B)

Solution and Explanation:

Approach Solution 1:

The problem statement informs that:

Given:

• A certain purse contains 30 coins
• Each coin is either a nickel or a quarter.
• The total value of all coins in the purse is 4.70$

Find out:

• The number of nickels the purse contains.

It is required to know the fact that each nickel is worth 5 cents ($0.05) and each quarter is worth 25 cents ($0.25).
Let the number of nickels in the purse be n.
This indicates the number of quarters in the purse = (30-n) (since there is a sum of 30 COINS)
Since each nickel is worth 5 cents, Therefore, we can say, n nickels are worth 5n cents.
Similarly, since each quarter is worth 25 cents, Therefore, we can say (30-n) quarters are worth 25(30-n) cents.
The total value of all coins in the purse is $ 4.70
Therefore, it means that the total value is 470 CENTS
Hence, we can write,
(value of all nickels) + (value of all quarters) = 470 CENTS
Or, 5n + 25(30-n) = 470
=> 5n + 750 - 25n = 470
=> -20n + 750 = 470
=> -20n = -280
Therefore, n = 14
Hence, the number of nickels the purse contains = 14.

Approach Solution 2:

The problem statement suggests that:
Given:

• A certain purse contains 30 coins
• Each coin is either a nickel or a quarter.
• The total value of all coins in the purse is 4.70$

Find out:

• The number of nickels the purse contains.

To solve the question, we must remember the fact that each nickel is worth 5 cents ($0.05) and each quarter is worth 25 cents ($0.25).
Let the number of nickels be n and the number of quarters is q.
As per the given condition in the question, we can derive two equations such as:
.25q+.05n=4.7 —-(i)
q+n=30 —-- (ii)
We need to find the value of n.
From equation (ii), we get:
q+n=30
q=30−n
Therefore, by putting the value of q in equation (i), we get
=>.25q+.05n=4.7
=>.25(30−n)+.05n=4.7
=> 7.5−.25n+.05n=4.7
=> 7.5−.2n=4.7
=> 7.5=4.7+.2n
=> 7.5−4.7=.2n
=> .2n= 2.8
=> n= 2.8/.2
=> n= 14

Hence, the number of nickels the purse contains = 14.

Approach Solution 3:

The problem statement suggests that:
Given:

• A certain purse contains 30 coins
• Each coin is either a nickel or a quarter.
• The total value of all coins in the purse is 4.70$

Find out:

• The number of nickels the purse contains.

It is required to mention the fact that each nickel is worth 5 cents ($0.05) and each quarter is worth 25 cents ($0.25)]
As per the conditions given in the question, we can make the money equation as
25q + 5n = 470 (where q= number of quarters and n= number of nickels)
Or, 5q + n = 94
Therefore, the coin equation is:
n + q = 30
Or, q = 30 - n
By substituting, we get:
5(30 - n) + n = 94
=> 150 - 5n + n = 94
=> 56 = 4n
=> n= 14
Hence, the number of nickels the purse contains = 14.

“A certain purse contains 30 coins, Each coin is either a nickel or''- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT Problem Solving questions measure the candidates’ content and logical understanding of basic concepts of mathematics. GMAT Quant practice papers present varieties of questions that will help to promote the mathematical knowledge of the candidates.

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