Question

Andy has 145 coins in his coin bank. THe number of 5-denomination coins is 10 more than twice the number of 10-denomination coins. The difference between the number of 1-denomination coins and 5-denomination coins is 5 more than the number of 10-denomination coins. How many of each kind of coin does he have?

Answer 1

tens = t
fives = f
ones = p
then
t+f+p = 145
f = 10+2t
p - f = 5 + t so p = 5+f +t
= 5 + 10+2t + t = 15+3t
so
t + 10+2t + 15+3t = 145

6 t + 25 = 145
6 t = 120
t = 20
p = 15+3(20) = 75
f = 10+2(20) = 50