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?
Let hundreds digit = x, then tens = x+5 and ones digit = 4x.
x + (x+5) + 4x = 17
Caculate for x, then x+5 and 4x.
986
Let's go step-by-step to find the mystery number based on the given information.
Step 1: The ones digit is 4 times the hundreds digit.
Let's represent the hundreds digit as "x".
The ones digit can be expressed as 4x.
Step 2: The tens digit is 5 more than the hundreds digit.
The tens digit can be expressed as x + 5.
Step 3: The sum of the digits is 17.
The sum of the digits can be computed as:
x + (x + 5) + 4x = 17
Step 4: Simplify the equation.
6x + 5 = 17
Subtract 5 from both sides:
6x = 12
Divide both sides by 6:
x = 2
Step 5: Find the tens digit.
The tens digit can be calculated as:
2 + 5 = 7
Step 6: Find the ones digit.
The ones digit can be calculated as:
4 * 2 = 8
Step 7: Assemble the mystery number.
The mystery number is 278.
Therefore, the mystery number is 278.
To find the mystery number, let's break down the given information 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 hundreds digit is x. In that case, the ones digit would be 4 times x, which is 4x.
3. "The tens digit is 5 more than the hundreds digit": This means the tens digit would be x + 5.
4. "The sum of the digits is 17": We can write this as an equation: x + (x + 5) + 4x = 17.
Now, let's solve the equation to find the value of x:
x + (x + 5) + 4x = 17
6x + 5 = 17
6x = 12
x = 2
So, the hundreds digit (x) is 2. Now let's find the tens and ones digit:
Tens digit = x + 5 = 2 + 5 = 7
Ones digit = 4x = 4 * 2 = 8
Therefore, the mystery number is 278.