SOLUTION: Marc Bryan is putting P1 and P5 coins in his piggy bank. The total amount inside is P145. The number of P1 is 1 more than 3 times the number of P5 coins. How many P1 and P5 coins a

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Question 169581: Marc Bryan is putting P1 and P5 coins in his piggy bank. The total amount inside is P145. The number of P1 is 1 more than 3 times the number of P5 coins. How many P1 and P5 coins are there?
please give me your representation.....
thank you
Answer by solver91311(24713) About Me  (Show Source):
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I'm presuming that you mean 1 penny and 5 pence coins, analogous to American penny and nickel. So let the NUMBER of penny coins be represented by p. Since each is worth one penny, the value of that number of coins is simply p as well. Let the number of P5 coins be represented by n (as in the American nickel). Since the value of each P5 coin is 5 pence, then the value of all the P5 coins would be 5n.

We are given that p = 3n + 1 (the number of P1 coins is one more than 3 times the number of P5 coins)

And we are given that p + 5n = 145 (the total amount inside is P145)

Rearranging:

Eq 1: p-3n=1
Eq 2: p%2B5n=145 which can also be represented Eq 3: -p-5n=-145

Add Equation 1 to Equation 3:

p-p-3n-5n=1-145
-8n=-144
n=18

So now we know that there are 18 P5 coins.

Since we know that the number of P1 coins is 3 times the number of P5 coins plus 1, we can say that there are 18%2A3%2B1=54%2B1=55 P1 coins.

Check:

The value of 18 P5 coins is P90 (5*18=90) and the value of 55 P1 coins is P55 (1*55=55) and P55 + P90 = P145 which matches the given total value in the problem. Done.