Final answer:
Rai could have $40 but not $42. The possible amounts of money Rai could have are multiples of 5 or odd multiples of 5 if fractional numbers of five-dollar bills are allowed.
Step-by-step explanation:
Let's assume Rai has x five-dollar bills. According to the question, he will have 3x one-dollar bills. To find the total amount of money Rai could have, we need to calculate the value of the five-dollar bills and the one-dollar bills.
The value of the x five-dollar bills would be 5x dollars. The value of the 3x one-dollar bills would be 3x dollars. The total amount of money Rai could have is the sum of these two values, which is 5x + 3x dollars.
To check if Rai could have $40, we need to solve the equation 5x + 3x = 40. Simplifying it gives us 8x = 40, and dividing both sides by 8 gives us x = 5. Therefore, Rai would need 5 five-dollar bills, which means he would have 15 one-dollar bills. The total amount of money Rai would have is 5*5 + 15*1 = 25 + 15 = $40. So yes, Rai could have $40.
Similarly, to check if Rai could have $42, we need to solve the equation 5x + 3x = 42. Simplifying it gives us 8x = 42, and dividing both sides by 8 gives us x = 5.25. Since x represents the number of five-dollar bills, it cannot be a decimal. Therefore, Rai cannot have $42.
From the calculations, we notice that the only possible amounts of money Rai could have are multiples of 5, such as $5, $10, $15, $20, and so on. Odd multiples of 5, such as $15 and $25, are also possible if we allow fractional numbers of five-dollar bills.