My 3rd grade son get this math problem.
It states that John thinks of a 3-digit number. What is his number? Use the clues below to find John's number.
Every digit is different.
The sum of all thedigits is 19.
The difference between the hundreds digit and the ones digit is 6.
The tens digit is the greatest digit.
The number is greater than 500.
Please Help.
Use trial and error.
The hundreds digit is 6, 7, 8, or 9
The ones digit is 0, 1, 2, or 3
The tens digit is 7, 8, or 9
Can you figure this out now?
if hundreds-ones=6, then we have
9x3
8x2
7x1
6x0
Since the digits add to 19, 7x1 and 6x0 are out, leaving
9x3 or 8x2
If tens is greatest, 9x3 is out, so we must have
892
This must be the number, since the only other choice would be 298, where the difference between hundreds and ones is still 6, but in the other direction
x y z
x + y + z = 19
|x-z| = 6
x >/= 5
y >/= 6
so x+y >/= 11
so z </= 8 to get 19 sum
z < 6 because y is biggest
choices
x 5 6 7 8 9
y 6 7 8 9
z 0 1 2 3 4 5 6 7 8
but x and z differ by 6 so
x 5 6 7 8 9
y 6 7 8 9
z 0 1 2 3
now what adds to 19 there with y biggest?
none until y = 9
so x 9 z
but x and z differ by six
8 and 2 differ by six
8 9 2 ?
To solve this math problem, we need to follow the clues provided and use logical reasoning.
Clue 1: Every digit is different.
This means that none of the three digits can be the same.
Clue 2: The sum of all the digits is 19.
Since we are dealing with a 3-digit number, we can express this as an equation:
Let's assume the three digits of John's number are A, B, and C.
A + B + C = 19
Clue 3: The difference between the hundreds digit and the ones digit is 6.
The hundreds digit minus the ones digit equals 6, or in equation form:
A - C = 6
Clue 4: The tens digit is the greatest digit.
This means the tens digit should be greater than both the hundreds and ones digits.
Clue 5: The number is greater than 500.
This tells us that the hundreds digit must be greater than 5.
Now let's solve the problem step by step using these clues:
1. We know that the sum of the three digits is 19, so A + B + C = 19.
2. The difference between the hundreds and ones digits is 6, so A - C = 6.
To simplify the problem, let's substitute one variable in terms of the other and solve for the remaining variable:
From A - C = 6, we can rewrite it as A = C + 6.
Now we substitute A in the equation A + B + C = 19:
(C + 6) + B + C = 19
Simplifying this equation, we get: 2C + B + 6 = 19
Now let's rearrange the equation: 2C + B = 13
Since the tens digit is the greatest digit, we know that B should be the largest possible digit, which is 9.
Now substitute B = 9 into the equation: 2C + 9 = 13
Simplifying further, we find: 2C = 4 => C = 2
Similarly, substitute C = 2 into the equation A = C + 6:
A = 2 + 6 => A = 8
Thus, we have determined that the hundreds digit is 8, the tens digit is 9, and the ones digit is 2.
Therefore, John's number is 892.