It’s less than 300
The ones digit 4 times the hundred digit
The tens digit is 5 more than the hundreds digit
The sum of the digits is 17
Let hundreds digit = x
The tens digit is 5 more than the hundreds digit means:
tens digit = x + 5
The ones digit 4 times the hundred digit means:
ones digit = 4 x
The sum of the digits is 17 means:
hundreds digit + tens digit + ones digit = 17
x + x + 5 + 4 x = 17
6 x + 5 = 17
Subtract 5 to both sides
6 x = 12
x = 12 / 6 = 2
hundreds digit = x = 2
tens digit = x + 5 = 2 + 5 = 7
ones digit = 4 x = 4 ∙ 2 = 8
Your number is:
278
The number starts with a 1 or 2, so it has the form
1?4 or 2?8
Since the digits sum to 17, and the maximum digit is 9, 1?4 is out
That just leaves 278
To find the number that satisfies all the given conditions, let's break down the problem step by step:
1. It's less than 300: This means that the hundreds digit cannot be equal to or greater than 3.
2. The ones digit is 4 times the hundreds digit: Let's denote the ones digit as "x" and the hundreds digit as "y". According to the condition, we have the equation x = 4y.
3. The tens digit is 5 more than the hundreds digit: Again, let's denote the tens digit as "z". According to the condition, we have the equation z = y + 5.
4. The sum of the digits is 17: The sum of all three digits can be expressed as x + y + z. According to the condition, we have the equation x + y + z = 17.
Now, let's use these equations to find the values of x, y, and z.
From equation 2, we can rewrite it as z - y = 5. Rearranging, we get y = z - 5.
Substituting the value of y in equation 1, we have x = 4(z - 5).
Substituting the values of x and y in equation 4, we get 4(z - 5) + (z - 5) + z = 17.
Simplifying equation 4, we have 6z - 21 = 17.
Adding 21 to both sides, we get 6z = 38.
Dividing both sides by 6, we find z = 6. Therefore, the tens digit is 6.
Using the value of z in equation 2, we have y = z - 5 = 6 - 5 = 1. Therefore, the hundreds digit is 1.
Using the value of y in equation 1, we have x = 4y = 4(1) = 4. Therefore, the ones digit is 4.
So, the number that satisfies all the given conditions is 146.