A copy machine accepts nickels, dimes, and quarters. After 1 hour, there are 30 coins total, and their value is $5.10. How many nickels, quarters, and dimes are in the machine? (Hint: There are exactly five different solutions.)

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Answer 1 · 2018-07-16T12:18:59

Possible numbers of nickel , dime and quarter coins are
#(0,16,14) or (3,12,15) or (6,8,16) or (9,4,17)# or(
#12,0,18)# respectively.

Worth of nickel , dime , quarter and dollar are #5,10,25 and 100#

cents respectively. Let the number of nickel and dime coins be

#x and y# respectively , then number of quarter coin is

#30-(x+y)# . Total worth of #30# coins is #510# cents.

#:. 5 x+10 y+ {30-(x+y)}25=510 # or

# 5 x+10 y-25 x-25 y +750=510# or

# 20 x+15 y = 240 or 5(4 x+ 3 y) =240 # or

#4 x+ 3 y =48 ; x and y # are whole numbers.

Possible combination of #x and y# are

#{(0,16) , (3,12), (6,8), (9,4) and (12,0)#

Therefore possible combination of #x ,y and 30-(x+y)# are

#{(0,16,14) , (3,12,15), (6,8,16), (9,4,17) and (12,0,18)#

Possible numbers of nickel , dime and quarter coins are

#(0,16,14) or (3,12,15) or (6,8,16) or (9,4,17)# or

#(12,0,18)# respectively [Ans]