Peter the postman was managing some letters.

Question

After mailing out 4/5 of his letters, he received 30 new ones. He then mailed out 1/6 of his letters and received 15 more letters. In the end, Peter had 70 letters.
How many letters did he have at first?

Answer 1

Let's assume Peter had x letters at first.
After mailing out 4/5 of his letters, he was left with 1/5 * x letters.
He then received 30 new letters, so he had 1/5 * x + 30 letters.
After mailing out 1/6 of his letters, he was left with 5/6 * (1/5 * x + 30) letters.
He also received 15 new letters, so he had 5/6 * (1/5 * x + 30) + 15 letters.
According to the given information, Peter had 70 letters at the end. Therefore, we can create the equation:
5/6 * (1/5 * x + 30) + 15 = 70
Multiplying both sides of the equation by 6/5 to eliminate the denominator:
(1/5 * x + 30) + 18 = 84
1/5 * x + 48 = 84
1/5 * x = 36
Multiplying both sides of the equation by 5 to solve for x:
x = 36 * 5
x = <<36*5=180>>180
Therefore, Peter had 180 letters at first. Answer: \boxed{180}.