1 PhP = 100 centavos

let

x = the number of five-centavo coins

y = the number of ten-centavo coins

she has 14 coins:

x + y = 14

the total value of the coins is Php 1.00 = 100 centavos:

5x + 10y = 100 divide both sides by 5

x + 2y = 20

by solving the system of equations:

x + y = 14

x + 2y = 20

we find:

x = 8 five-centavo coins

y = 6 ten-centavo coins

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Mary has 8 five-centavo and 6 ten-centavo coins.