Mrs. Rossi wrote the following clus for a mystery 4-digit number.
.The tens digit is twice the one digit
.The hundreds digit is twice the ones digit.
.The ones digit is 3.
.The sum of the digits is 19.
What is the mystery number?
show the work.
If the ones digit = 3, then as twice as large, the hundreds and tens digits = 6
x+ 6 + 6 + 3 = 19
Solve for x.
To find the mystery 4-digit number, let's assign variables to each digit:
Let the thousands digit be represented by 'A'
Let the hundreds digit be represented by 'B'
Let the tens digit be represented by 'C'
Let the ones digit be represented by 'D'
Based on the given clues, we can set up the following equations:
1) "The tens digit is twice the ones digit":
C = 2D
2) "The hundreds digit is twice the ones digit":
B = 2D
3) "The ones digit is 3":
D = 3
4) "The sum of the digits is 19":
A + B + C + D = 19
Now, let's substitute the values from clue 3 into equations 1 and 2:
C = 2(3) = 6
B = 2(3) = 6
Our equations now look like this:
1) C = 6
2) B = 6
3) D = 3
4) A + B + C + D = 19
Substituting the values for B, C, and D into the fourth equation, we get:
A + 6 + 6 + 3 = 19
Combining like terms, we have:
A + 15 = 19
Subtracting 15 from both sides of the equation, we get:
A = 4
So, the thousands digit (A) is 4, the hundreds digit (B) is 6, the tens digit (C) is 6, and the ones digit (D) is 3.
Therefore, the mystery number is 4,663.