The sum of the of a two-digit number is 15. One third of the number diminished by 12 is 17. Find the number.
Did you mean the "sum of the digits of a two-digit number is 15" ?
if so, then
let the unit digit be x
let the tens digit be y
so the value is 10y + x
"One third of the number diminished by 12 is 17"
---> (1/3)(10y+x) - 12 = 17
(1/3)(10y+x) = 29
multiply by 3
10y+x = 87
x = 87 - 10y
also x+y = 15
by substitution:
87-10y + y = 15
-9y = -72
y = 8
x = 87 - 80 = 7
the number is 87
check the properties stated.
Well, solving a math problem through humor? Now that's a challenge! Let's give it a shot.
Let's call the tens digit of the two-digit number 'x' and the units digit 'y'. So, the number can be represented as 10x + y.
We have two conditions here. First, the sum of the digits is 15. That means x + y = 15. Alright, we're halfway there.
Now, the second condition states that one-third of the number diminished by 12 is 17. In equation form: (1/3)(10x + y) - 12 = 17.
Hmm, let's simplify that equation a bit. 10x + y - 36 = 51.
Now we have a system of two equations:
x + y = 15
10x + y = 87
Alright, time to solve this puzzle. Let me put on my clown mathematician hat. *puts on oversized hat* Okay, let's solve this using the substitution method.
From the first equation, we can express y in terms of x: y = 15 - x.
Now, substitute this value of y into the second equation: 10x + (15 - x) = 87.
Combining like terms, we get: 9x + 15 = 87.
Subtracting 15 from both sides, we have: 9x = 72.
And finally, dividing both sides by 9, we find: x = 8.
Now that we know x, we can go back to the first equation: 8 + y = 15.
Subtracting 8 from both sides, we find: y = 7.
So, the two-digit number is 87! *throws confetti* Ta-da! We did it!
Let's solve this step by step.
Step 1: Let's suppose the two-digit number is represented by 'xy', where x represents the tens digit and y represents the units digit.
Step 2: The sum of the digits is given as 15. Therefore, we have the equation x + y = 15.
Step 3: One third of the number, diminished by 12, is 17. Mathematically, we can represent this as (xy / 3) - 12 = 17.
Step 4: Simplifying the equation, we get xy / 3 = 17 + 12.
Step 5: Combining like terms, we have xy / 3 = 29.
Step 6: Multiplying both sides of the equation by 3 to get rid of the fraction, we have xy = 87.
Step 7: From Step 6, we can conclude that the two-digit number is 87.
Therefore, the number is 87.
To solve this problem, we'll use algebraic equations. Let's call the tens digit of the two-digit number 'x' and the units digit 'y'.
The first clue states that the sum of the two digits is 15, which can be represented as:
x + y = 15 ... Equation (1)
The second clue states that one third of the number diminished by 12 is 17, which can be represented as:
(10x + y)/3 - 12 = 17 ... Equation (2)
To simplify Equation (2), we can multiply both sides by 3 to eliminate the fraction:
10x + y - 36 = 51
Now, let's rearrange this equation:
10x + y = 87 ... Equation (3)
We have a system of equations with equations (1) and (3). We can solve this system by substitution or elimination method.
Let's use the elimination method. Multiply Equation (1) by 10 to make the variable 'x' match with Equation (3):
10x + 10y = 150 ... Equation (4)
Subtract Equation (4) from Equation (3):
(10x + y) - (10x + 10y) = 87 - 150
y - 10y = -63
-9y = -63
Divide both sides by -9:
y = 7
Now, substitute the value of 'y' into Equation (1) to find 'x':
x + 7 = 15
x = 15 - 7
x = 8
So, the two-digit number is 87.