Question

dave collected 30% more stamps than John. dave gave away 15% of his stamps while john gave away 60% of his stamps. John had 282 fewer stamps than dave in the end .how many stamps did dave have at first.

Answer 1

Dave initially had 520 stamps. John started with 400 stamps, and after giving away their respective percentages, Dave has 282 stamps more than John.

Step-by-step explanation:

To find out how many stamps Dave had at first, let's denote the number of stamps John starts with as J. If Dave collected 30% more stamps than John, then Dave had 1.3J stamps initially. After Dave gave away 15% of his stamps, he was left with 85% of his original number, which is 1.3J × 0.85. John, on the other hand, gave away 60% of his stamps, leaving him with 40% of his original number, which is J × 0.40.

In the end, John has 282 fewer stamps than Dave, which gives us the equation: 1.3J × 0.85 - J × 0.40 = 282. Simplifying this equation, we multiply out the percentages to get: 1.105J - 0.4J = 282, which further simplifies to 0.705J = 282. Dividing both sides by 0.705, we find J = 282 / 0.705, which gives us J = 400. Finally, to find the number of stamps Dave had initially, we calculate 1.3× 400, which is 520 stamps.