Thank you in advance for helping me.  

asked Sep 21, 2015 in Algebra 2 Answers by anonymous

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William has $4.20 in his bank in nickels, dimes and quarters. has 44 coins. number of nickels is one more than twice the number of dimes. Find the number of each kind of coin he has.
Thank you in advance for helping me.  

N = number of nickels
D = number of dimes
Q = number of quarters

N = 2D + 1
Q = 44 - (D + N)
Q = 44 - (D + (2D + 1)
Q = 44 - (3D + 1)
Q = 44 - 3D - 1
Q = 43 - 3D

0.05N + 0.10D + 0.25Q = 4.20
0.05(2D + 1) + 0.10D + 0.25(43 - 3D) = 4.20
0.10D + 0.05 + 0.10D + 10.75 - 0.75D = 4.20
-0.55D + 10.80 = 4.20
-0.55D = -6.60
D = -6.60/-0.55
D = 12    <<<<<<<<<<<<<<<<<<<<<<  number of dimes

N = 2D + 1
N = 2(12) + 1
N = 25    <<<<<<<<<<<<<<<<<<<<<< number of nickels

Q = 44 - D - N
Q = 44 - 12 - 25
Q = 7    <<<<<<<<<<<<<<<<<<<<<< number of quarters

$D = 0.10 * 12 = $1.20
$N = 0.05 * 25 = $1.25
$Q = 0.25 *  7 = $1.75
                          --------
                          $4.20

It all checks.
answered Sep 21, 2015 by CWA Level 11 User (78,600 points)

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