Answer:
The number of 50 notes = 6
The number of 20 notes = 10
The number of 10 notes = 9
Explanation:
The given parameters are;
The total amount Kevin has as currency = 590
The denominations of the notes Kevin has = 50, 20, and 10
The ration of the 50 notes and the 20 notes = 3:5
The total number of notes he has = 25
Therefore, we have;
Let 'x', 'y', and 'z' represent the numbers of 50, 20, and 10 notes Kevin has respectively, we are given the following;
x/y = 3/5...(1)
x + y + z = 25...(2)
50·x + 20·y + 10·z = 590...(3)
Therefore, from equation (1) we get;
x = 3·y/5
By substituting the value of x = 3·y/5 in equations (2) and (3), we get;
For equation (2), we get
x + y + z = 3·y/5 + y + z = 8·y/5 + z = 25
z = 25 - 8·y/5
For equation (3), we get;
50·x + 20·y + 10·z = 50·(3·y/5) + 20·y + 10·z = 50·y + 10·z = 590
∴ z = (590 - 50·y)/10 = 59 - 5·y
Equating the two values of 'z' gives;
25 - 8·y/5 = 59 - 5·y
5·y - 8·y/5 = 59 - 25 = 34
17·y/5 = 34
y = 34/17 × 5 = 10
y = 10
x = 3·y/5 = 3 × 10/5 = 6
x = 6
z = 59 - 5·y = 59 - 5 × 10 = 9
z = 9
Therefore, Kevin has 6, 50 notes, 10, 20 notes and 9, 10 notes