exploring mathematics elementary algebra....the sum of the digits of a two-digit number is 12. the value of the number is equal to 11 times the tens digit. find the number.
Assistance needed.
let the unit digit be x
let the tens digit be y
so the "value" of the two digit number is 10y + x
and then you said:
10y + x = 11y
x = y
but we also know x+y = 12
mmmh? Can you think of two numbers that are equal and add up to 12 without doing the algebra?
To find the two-digit number, let's go step by step:
Let's assume the tens digit is x and the units digit is y. Therefore, the two-digit number can be expressed as 10x + y.
According to the problem, the sum of the digits of the two-digit number is 12. Hence, we can set up the equation:
x + y = 12 (Equation 1)
The problem also states that the value of the number is equal to 11 times the tens digit. Therefore, we have:
10x + y = 11x (Equation 2)
Now, let's solve this system of equations by substituting Equation 1 into Equation 2:
10x + y = 11x
10x + (12 - x) = 11x
10x + 12 - x = 11x
9x + 12 = 11x
To eliminate the variable on the right side, we'll subtract 9x from both sides:
12 = 11x - 9x
12 = 2x
Next, divide both sides by 2:
12/2 = x
6 = x
So, the tens digit, x, is equal to 6.
Now, substitute x = 6 back into Equation 1 to find the value of y:
6 + y = 12
y = 12 - 6
y = 6
Therefore, the units digit, y, is 6.
Thus, the two-digit number is 10x + y, which gives us:
Number = 10(6) + 6
Number = 60 + 6
Number = 66
Hence, the number is 66.