Ravi had a total of 80 pieces of $10 notes and $50 notes. He used 1/2 of his $10 notes and withdrew another 8 pieces of $50 from the bank. After which, the number of $50 notes he had became 2/5 of the number of $10 notes. Find the total value of the 80 pieces of notes that he had at first

1 answer

Let's start by finding the number of $10 notes that Ravi had initially.
Let the number of $10 notes be x.
Since he used 1/2 of the $10 notes, he now has x - 1/2*x = 1/2*x notes remaining.
The total number of $10 notes remaining is 80 - 1/2*80 = 40.
He also withdrew 8 pieces of $50 notes from the bank, so the number of $50 notes he had now is 1/2*x + 8.
According to the problem, the number of $50 notes now is 2/5 of the number of $10 notes, so we can write the equation:
1/2*x + 8 = 2/5*x.
Multiplying both sides of the equation by 10 to get rid of the fractions, we have:
5*(1/2*x + 8) = 5*(2/5*x).
Simplifying the equation, we get:
5/2*x + 40 = 4/5*x.
Multiplying both sides of the equation by 10 to get rid of the fractions, we have:
25*x + 400 = 8*x.
Moving all the terms to one side of the equation, we have:
17*x = 400.
Dividing both sides of the equation by 17, we have:
x = 400/17 = 23.53 (rounded to two decimal places).
Since the number of notes must be a whole number, we round x to the nearest whole number, x = 24.
Therefore, Ravi initially had 24 $10 notes.
Since he had a total of 80 notes, the number of $50 notes he initially had is 80 - 24 = 56.
The total value of the 80 pieces of notes that Ravi had at first is 24*10 + 56*50 = $<<24*10+56*50=3320>>3320. Answer: \boxed{3320}.