Swapnil has rs590 in currency notes with denominations of rs 50,rs20,rs10. The ratio of the number of rs.50 notes and rs.20 notes is 3 :5. If he has total of 25 notes how many notes of each denomination does he have
To find the number of notes of each denomination, we need to determine the value of the rs.50 notes and rs.20 notes according to the given ratio.
Let's assume the number of rs.50 notes is 3x, and the number of rs.20 notes is 5x.
The value of each rs.50 note is rs.50, so the total value of the rs.50 notes is 50 * (3x) = 150x.
Similarly, the value of each rs.20 note is rs.20, so the total value of the rs.20 notes is 20 * (5x) = 100x.
We can set up the equation for the total value of the notes:
150x + 100x + (10 * remaining notes) = 590
Where "remaining notes" is the number of rs.10 notes.
Now, let's determine the value of the rs.10 notes based on the given information.
The total number of notes is given as 25. So, we have:
3x + 5x + remaining notes = 25
Combining this equation with the previous one:
150x + 100x + (10 * (25 - (3x + 5x))) = 590
Simplifying the equation:
150x + 100x + (10 * (25 - 8x)) = 590
Combine like terms:
250x + (10 * (25 - 8x)) = 590
Distribute the 10:
250x + 250 - 80x = 590
Combine like terms again:
170x + 250 = 590
Subtract 250 from both sides:
170x = 340
Divide both sides by 170:
x = 2
Now that we know the value of x, we can find the number of notes for each denomination:
Number of rs.50 notes = 3x = 3 * 2 = 6
Number of rs.20 notes = 5x = 5 * 2 = 10
Number of rs.10 notes = 25 - (3x + 5x) = 25 - (3 * 2 + 5 * 2) = 25 - (6 + 10) = 25 - 16 = 9
Therefore, Swapnil has 6 notes of rs.50, 10 notes of rs.20, and 9 notes of rs.10.
let the number of 50 notes be 3x
let the number of 20 notes be 5x , notice they are in 3:5 ratio
number of 10 notes = 25 - 3x - 5x or 25 - 8x
value of notes equation:
50(3x) + 20(5x) + 10(25-8x) = 590
150x + 100x + 250 - 80x = 590
170x = 340
x = 2
sub back into my definitions