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Question 21514: a coins collection consists of 4, 2, and 3 cent coins. the number of 2 cent coin is one less than twice the number of 4 cent coins. the number 3 cent coins is five more than the number of 2 cent coins. the total value of all coins is $3.00 find the number of 2 cent coins in the collection.
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! a coins collection consists of 4, 2, and 3 cent coins. the number of 2 cent coin is one less than twice the number of 4 cent coins. the number 3 cent coins is five more than the number of 2 cent coins. the total value of all coins is $3.00 find the number of 2 cent coins in the collection.
LET THE NUMBER OF 4 CENT COINS =X
TWICE THIS =2X
ONE LESS THAN THIS =2X-1 ..THIS IS EQUAL TO NUMBER OF 2 CENT COINS
5 MORE THAN THIS =2X-1+5=2X+4..THIS IS EQUAL TO NUMBER OF 3 CENT COINS
SO TOTAL VALUE OF COINS =4X+2(2X-1)+3(2X+4)=4X+4X-2+6X+12
=14X+10...THIS EQUAL TO $3 OR 300 CENTS
HENCE 14X+10=300
14X=300-10=290
X=290/14..THERE IS A MISTAKE IN NUMBERS SINCE X IS COMING A FRACTION
LET US TAKE $2.90 INSTEAD OF $3 TO ILLUSTRATE THE ANSWER.
WE GET 14X+10=290 CENTS
14X=290-10=280
X=280/14=20
HENCE THERE ARE 2O COINS OF 4 CENTS ...................OF VALUE =20*4=80 CENTS
NUMBER OF 2 CENT COINS =2X-1=2*20-1=40-1=39............OF VALUE =39*2=78 CENTS
NUMBER OF 3 CENT COINS = 2X+4=2*20+4=40+4=44...........OF VALUE=44*3=132 CENTS
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TOTAL VALUE .........................................................290 CENTS
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