SOLUTION: A coin bank for donations for the protection of the reef contained ₱1570. There were twice as many ₱5-coins as ₱10- coins, and 14 less ₱1-coins as ₱5-coins. How many of

Algebra ->  Angles -> SOLUTION: A coin bank for donations for the protection of the reef contained ₱1570. There were twice as many ₱5-coins as ₱10- coins, and 14 less ₱1-coins as ₱5-coins. How many of       Log On


   

Question 1192213: A coin bank for donations for the protection of the reef contained ₱1570. There were twice as many ₱5-coins as ₱10-
coins, and 14 less ₱1-coins as ₱5-coins. How many of each kind were there?
Answer by ikleyn(52778) About Me  (Show Source):
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A coin bank for donations for the protection of the reef contained ₱1570. There were twice as many ₱5-coins as ₱10-
coins, and 14 less ₱1-coins as ₱5-coins. How many of each kind were there?
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Let x be the number of P10-coins.

Then the number of P5-coins is 2x and the number of P1-coins is (2x-14).


Now write the total money equation

    10x + 5*(2x) + 1*(2x-14) = 1570.


Simplify and find x

    10x + 10x + 2x - 14 = 1570

         22x            = 1570 + 14

         22x            = 1584

           x            = 1584/22 = 72.


ANSWER.  There are  72  P10-coins;  722*2 = 144  P5-coins  and  144 - 14 = 130 P1-coins.


CHECK.  10*72 + 5*144 + 130 = 1570,  total money.   ! Correct !

Solved.