Question 1149415
<br>
----------------------------------------------------<br>
Edited response -- I used 25-cent (American) instead of 20-cent (UK?) coins.<br>
According to the defined process....<br>
(1) dollar coins<br>
Every multiple of 5 will have a dollar coin.
120/5 = 24
24 dollar coins<br>
(2) 50-cent coins<br>
Every multiple of 4 that is not also a multiple of 5 will have a 50-cent coin, so number of multiples of 4 minus number of multiples of 4*5=20.
120/4 = 30
120/20 = 6
30-6 = 24 50-cent coins<br>
(3) {{{cross(25-cent)}}} 20-cent coins<br>
Every multiple of 3 that is not also a multiple of 4 and/or 5 will have a {{{cross(25-cent)}}} 20-cent coin -- so number of multiples of 3, minus number of multiples of 3*4=12, minus number of multiples of 3*5=15, PLUS number of multiples of 3*4*5=60.
120/3 = 40
120/12 = 10
120/15 = 8
120/60 = 2
40-10-8+2 = 24 {{{cross(25-cent)}}} 20-cent coins<br>
(4) 10-cent coins<br>
This case was going to require complicated calculations, so I will determine the number of 5-cent coins; then what is left is 10-cent coins.<br>
(5) 5-cent coins<br>
(a) the number 1 (1 number)
(b) all primes greater than 5 and less than 120 (27 numbers)
(c) all numbers less than 120 with no prime factors 5 or less (7*7, 7*11, 7*13, 7*17; 4 numbers)
1+27+4 = 32 5-cent coins<br>
(4) 10-cent coins, revisited:<br>
120-(24+24+24+32) = 16 10-cent coins<br>
So we have...
24 dollar coins
24 50-cent coins
24 {{{cross(25-cent)}}} 20-cent coins
10 10-cent coins
32 5-cent coins<br>
The total value of the coins in cents is then<br>
{{{cross(24(100)+24(50)+24(25)+16(10)+32(5) = 4520)}}}
{{{24(100)+24(50)+24(20)+16(10)+32(5) = 4400)}}}<br>
I confirmed that answer using an excel file....<br>