Ibrahim and Richard had some money. After Ibrahim spent 2/5 of his money and Richard spent 4/9 of his money, they had the same amount of money left. If Richard had $300 more than Ibrahim, how much did Ibrahim spend?

1 answer

Let's start by using variables to represent the amount of money Ibrahim and Richard had. Let I be Ibrahim's amount and R be Richard's amount.
After Ibrahim spent 2/5 of his money, he had 3/5 of his money left. Similarly, after Richard spent 4/9 of his money, he had 5/9 of his money left. We know that they had the same amount of money left, so we can set up an equation:
3/5 I = 5/9 R
We also know that Richard had $300 more than Ibrahim, so we can set up another equation:
R = I + 300
Now we can substitute the second equation into the first equation to solve for I:
3/5 I = 5/9 (I + 300)
Multiplying both sides by 45 (the least common multiple of 5 and 9) to get rid of the fractions, we get:
27I = 25(I + 300)
Expanding the brackets, we get:
27I = 25I + 7500
Subtracting 25I from both sides, we get:
2I = 7500
Dividing both sides by 2, we get:
I = 3750
So Ibrahim had $3750 to start with. We can use the second equation to find out how much Richard had:
R = I + 300 = 3750 + 300 = 4050
Now we can check if our solution is correct. After Ibrahim spent 2/5 of his money, he had 3/5 of $3750 = $2250 left. After Richard spent 4/9 of his money, he had 5/9 of $4050 = $2550 left. Indeed, they have the same amount of money left. And we can also see that Richard had $300 more than Ibrahim ($4050 - $3750 = $300). Therefore, Ibrahim spent the difference between his starting amount and what he had left:
3750 - 2250 = 1500
So Ibrahim spent $1500.