Rahul and Rohan have 45 marbles together. After losing 5 marbles each, the product of the number of marbles they both have now is 124. How to find out how many marbles they had to start with.
Question
Rahul and Rohan have 45 marbles together. After losing 5 marbles each, the product of the number of marbles they both have now is 124. How to find out how many marbles they had to start with.
Solution
Sure, here is the step by step solution:
Step 1: Rahul and Rohan initially had 45 marbles together. After losing 5 marbles each, they now have 45 - 5 - 5 = 35 marbles together.
Step 2: Let's assume Rahul has x marbles now and Rohan has 35 - x marbles (since together they have 35 marbles).
Step 3: According to the problem, the product of the number of marbles they both have now is 124. So, we can set up the equation: x * (35 - x) = 124.
Step 4: This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = -1, b = 35, and c = -124.
Step 5: Solve this quadratic equation to find the value of x. The solutions of the equation are x = 7 and x = 28.
Step 6: So, Rahul could have 7 or 28 marbles now, and Rohan could have 28 or 7 marbles now.
Step 7: Since they lost 5 marbles each, initially, Rahul could have 7 + 5 = 12 or 28 + 5 = 33 marbles, and Rohan could have 28 + 5 = 33 or 7 + 5 = 12 marbles.
So, the possible initial number of marbles Rahul and Rohan could have had are (12, 33) or (33, 12).
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