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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.
by Level 11 User (78.4k points)

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