In a collection of nickels, dimes, and quarters worth $6.90, the ratio of the number of nickels to dimes is 3:8. The ratio of the number of dimes to quarters is 4:5. Find the number of each type of coin.

N=number of nickels

d=number of dimes

q=number of quarters

example

if n:d=3:8

lets say n=3 and d=8

3*8=8*3

so

8n=3d

slightly confusing but go with it, it migh make sense or it might not

n:d=3:8

8n=3d

d:q=4:5

5d=4q

solve for one of them

solve for nickels in first and quarters in second

8n=3d, n = (3/8) d

5d=4q, (4/5) d=q

5n+10d+25q=690

divide by 5 to make it easeir

n+2d+4q=138

sub (3/8) d for n

sub (4/5) d for q

(3/8) d+2d+5 (5/4) d=138

(3/8) d+2d+25/4d=138

3/8+2+25/4=

3/8+16/2+50/8=

69/8

(69/8) d=138

times both sides by 8

69d=1104

divide both sides by 69

d=16

16 dimes

sub back

(5/4) d=q

(5/4) 16=q

80/4=q

20=q

(3/8) d=n

(3/8) 16=n

48/8=n

6=n

6 nickles

16 dimes

20 quarters

yah