It is less than 300. The ones digit is 4 times the hundreds digit. The tens digit is 5 more than the hundreds digit. The sum of the digits is 17. What is the mystery number?
To find the mystery number, let's break down the information given step by step.
1. "It is less than 300": This means the mystery number is a two-digit number.
2. "The ones digit is 4 times the hundreds digit": Let's assume the ones digit is x, and the hundreds digit is y. According to the statement, x = 4y.
3. "The tens digit is 5 more than the hundreds digit": Let's call the tens digit z. The statement tells us z = y + 5.
4. "The sum of the digits is 17": The sum of the digits, x + y + z, is equal to 17.
Now, let's simplify the equations and find the values of x, y, and z.
From equation 2, we have x = 4y. Substituting this into equation 4, we get 4y + y + z = 17.
Combining like terms, we have 5y + z = 17 (equation 5).
From equation 3, we have z = y + 5. Substituting this into equation 5, we get 5y + (y + 5) = 17.
Simplifying further, we have 6y + 5 = 17.
Subtracting 5 from both sides, we get 6y = 12.
Dividing both sides by 6, we find y = 2.
Now that we know y, we can substitute it into equation 2 to find x: x = 4 * 2, which means x = 8.
Lastly, using equation 3, we substitute y = 2 into z = y + 5, giving us z = 2 + 5, which means z = 7.
Putting all the digits together, we find the mystery number is 782.
So, the mystery number is 782.