1. David recently had a garage sale and has amassed a pile of change. How many of each coin (penny, nickel, dime, quarters) does he have if:

Question

a.There is at least 5 pennies, 5 nickels, 5 dimes and 5 quarters
b.There is only a prime number of each coin
c.The total value is $5.75
d.There is a total of 40 coins

I need help figuring this out, please help.

Answer 1

p+5n+10d+25q = 575
p+n+d+q = 40

Now you know that there are
5,7,11,13,17,19,23 as the number of each coin.

Since there are no odd cents, you know that p=5.

Now you have

5n+10d+25q = 570
n+d+q = 35
or,
n+2d+5q = 114
n+d+q = 35

subtracting, we have
d+4q = 79

4q must be 20,28,44,52,68,76
That means d is 59,51,35,27,11,3
But we know that d<40 and d is prime, so d=3 or 11

If
d=3, q=19, p=5 so n=13
and the value is 575

If
d=11, q=17, p=5 so n=7
again, the value is 575