Question 46980: John has 24 coins in his pocket-nickels, dimes and quarters-amounting to $3.80. If he has twice as many nickels as quarters, how many dimes does he have?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! John has 24 coins in his pocket-nickels=N SAY, dimes=D SAY and quarters=Q SAY-amounting to $3.80. If he has twice as many nickels as quarters, how many dimes does he have?
N+D+Q=24............I
N+5D+25Q=380...........II
EQN.II-EQN.I...
4D+24Q=380-24=356.DIVIDING WITH 4...
D+6Q=89......................III
THERE ARE 2 UNKNOWNS AND ONLY ONE EQN. BUT THERE IS A PHYSICL FACT THAT N,D,Q MUST BE POSITIVE INTEGERS..HENCE TRY IN EQN.III...D=1,2,3 ETC,TO GET INTEGRAL ANSWERS
D=1..1+6Q=89...........6Q=88...BUT THIS WILL MAKE Q FRACTION.HENCE NOT POSSIBLE
SIMILARLY.....D=2,3,4 ARE NOT POSSIBLE
D=5.....5+6Q=89....6Q=84....Q=84/6=14...SO D=5,Q=14 AND N=24-14-5=5
FURTHER TRIALS FOR D=11....WILL LEAD TO 11+6Q=89....6Q=78...Q=13...THEN N=24-13-11=0..BUT WE ARE GIVEN THAT THERE ARE SOME NICKELS..HENCE ONLY SOLUTION IS
N=5=5 CENTS
D=5=5*5=25 CENTS
Q=14=14*25=350 CENTS
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TOTAL=24 COINS WITH VALUE OF 380 CENTS=$3.80
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