SOLUTION: Dante has Php19.50 in coins. if there were twice as many 5-centavos coins as 25-centavo coins, and as many 10-centavo coins as 5-centavo coins and 25 centavo coins combined, how ma

Dante has Php19.50 in coins. if there were twice as many 5-centavos
coins as 25-centavo coins, and as many 10-centavo coins as 5-centavo 
coins and 25 centavo coins combined, how many coins of each type 
were there?

Let x = the number of 25-centavo coins

>>...twice as many 5-centavos coins as 25-centavo coins...<<

Therefore the number of 5-centavo coins is 2x

>>...as many 10-centavo coins as 5-centavo coins and 25 centavo
coins combined...<<

Therefore the number of 10-centavo coins is their sum, or x + 2x,
which simplifies to 3x 

So, we have

x   25-centavo coins worth 25x centavos.
2x   5-centavo coins worth 5(2x)centavos, or 10x centavos.
3x  10-centavo coins worth 10(3x), or 30x centavos.

Their total is worth Php19.50, which is 1950 centavos.

So 
     x + 2x + 3x = 1950
              6x = 1950
               x = 325 25-centavo coins

              2x = 2(325) = 650 5-centavo coins
              3x = 3(325) = 975 10-centavo coins

Edwin