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B
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Difficulty:
35%
(medium)
Question Stats:
73% (02:08) correct
27%
(02:17)
wrong
based on 307
sessions
History
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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?
A. 12
B. 14
C. 16
D. 20
E. 22
A. 12
B. 14
C. 16
D. 20
E. 22
15 Dec 2017, 16:30
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Bookmarks
NATABERI
ASIDE: Each nickel is worth 5 cents ($0.05) and each quarter is worth 25 cents ($0.25)
Let n = the number of nickels in the purse
This means (30-n) = the number of quarters in the purse (since there is a total of 30 COINS)
Since each nickel is worth 5 cents, we know that n nickels is worth 5n CENTS
Likewise, since each quarter is worth 25 cents, we know that (30-n) quarters is worth 25(30-n) CENTS
The total value of all coins in the purse is $ 4.70
We can also say that the TOTAL value is 470 CENTS
So, we can write: (value of all nickels) + (value of all quarters) = 470 CENTS
Or: 5n + 25(30-n) = 470
Expand: 5n + 750 - 25n = 470
Simplify: -20n + 750 = 470
Subtract 750 from both sides: -20n = -280
Solve: n = 14
Answer: B
Cheers,
Brent
General Discussion
17 Nov 2014, 08:23
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NATABERI
To frame this as an equation:
n = number of nickels
q = number of quarters
1) \(.25q + .05n = 4.7\)
2) \(q + n = 30\)
So now you just need to solve for n.
\(q + n = 30\)
\(q = 30 - n\)
\(.25q + .05n = 4.7\)
\(.25(30-n) + .05n = 4.7\)
\(7.5 - .25n + .05n = 4.7\)
\(7.5 - .2n = 4.7\)
\(7.5 = 4.7 + .2n\)
\(7.5 - 4.7 = .2n\)
\(2.8 = .2n\)
\(2.8/.2 = n\)
\(14 = n\)
There are 14 nickels in the purse.
