SOLUTION: A coin purse contains 5 centavos, 10 centavos and 25 centavo coins. The number of 10 centavo coins is three times as many 5 centavo coins, and the 25 centavo coins is 2 more than t

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Question 697851: A coin purse contains 5 centavos, 10 centavos and 25 centavo coins. The number of 10 centavo coins is three times as many 5 centavo coins, and the 25 centavo coins is 2 more than the 10 centavo coins. If the total value of its content is $4.90, how many of each kind of coins are there in purse?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of 5 c coins
Let +b+ = number of 10 c coins
Let +c+ = number of 25 c coins
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given:
(1) +5a+%2B+10b+%2B+25c+=+490+
(2) +b+=+3a+
(3) +c+=+b+%2B+2+
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(2) +a+=+b%2F3+
Substitute (2) and (3) into (1)
(1) +5%2A%28b%2F3%29+%2B+10b+%2B+25%2A%28+b+%2B+2+%29+=+490+
(1) +5%2A%28+b%2F3+%29+%2B+10b+%2B+25b+%2B+50+=+490+
(1) +%285%2F3%29%2Ab+%2B+35b+=+440+
Multiply both sides by +3+
(1) +5b+%2B+105b+=+1320+
(1) +110b+=+1320+
(1) +b+=+12+
and, since
(2) +a+=+b%2F3+
(2) +a+=+12%2F3+
(2) +a+=+4+
and
(3) +c+=+b+%2B+2+
(3) +c+=+12+%2B+2+
(3) +c+=+14+
There are 4 of the 5 c coins
There are 12 of the 10 c coins
There are 14 of the 25 c coins
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check answer:
(1) +5a+%2B+10b+%2B+25c+=+490+
(1) +5%2A4+%2B+10%2A12+%2B+25%2A14+=+490+
(1) +20+%2B+120+%2B+350+=+490+
(1) +490+=+490+
OK