Answer :

Let n represents the number of nickel

Let p represents the number of pennies

Let d represents the number of dimes

Let q represents the number of quarters

Recall that

1 nickel = $0.05

1 penny = $0.01

1 dime = $0.1

1 quarter = $0.25

From the information given,

n + p + d + q = 12-------------------------------------------------(1)

0.05n + 0.01p + 0.1d + 0.25q = 1.67-------------------------(2)

p = n --------------------------------------------------------------------(3)

n + d = q ----------------------------------------------------------------(4)

Solving the four equations simultaneously, we have

Substitute equations (3) and (4) into equations (1) and (2)

n + n + d + n + d = 12

0.05n + 0.01n + 0.1d + 0.25(n + d) = 1.67

3n + 2d = 12-----------------------------------------(5)

0.31n + 0.35d = 1.67--------------------------------(6)

multiply equation (6) by 200 and equation (5) by 35, we have

105n + 70d=420------------------(7)

62n + 70d =334--------------------(8)

subtract equation (8) from (7)

43n = 86

n=86/43

n=2

put n=2 into equation (8)

62(2) + 70d = 334

124 + 70d = 334

70d = 334 - 124

70d = 210

d = 210/70

d=3

but p = n = 2

p = 2

n + d = q

q = 2 + 3 = 5

Hence, max have

2 nickels, 2 pennies, 3 dimes, 5 quarters

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