Answer :
Answer: ONLY 15, and 24 there are not more 2 digit triply numbers i have checked all the 2 digits numbers ranging from 10 to 99
Yes there are only 2 triply numbers! Isnt it shocking! I have tried for 2 digit triply numbers from 10 to 99! Yes i did that! Lets go through a basic idea first the product of its digits mean that you mulitply whatever number your checking for a triply number. Example: your checking 15 for a triply number so 1 x 5 = 5 ( you multiply the digits in the 2 digit number to find the product of its digit)! What does 3 times the product of its digits then? hmmmmm. we know that 15's product of its digit is 5 so we mulitiply 5 x 3 because it says three times the product of its digits.
Step-by-step explanation:
15 = 1 x 5 = 5 (we do 1 x 5 because we need to find the product of its digits and to do that we multiply the digits together in the 2 digit number).
5 x 3 = 15 (we multiplied 15 x 3 because it says 3 times the product of its digits. we know the product is 5 and 3 times is multiply by 3 so we do 5 x 3 which equals to 15).
So 15 is a triply number because in the second step when we multiplied 5 x 3 we got 15; and we were checking if 15 was a triply number; because we got 15 as the answer in the second step it is a triply number).
24 = 2 x 4 = 8
8 x 3 = 24
so we got 24 as the answer again in the second step which means that 24 is a triply number.
In short, you multiply the digits in the number then whatever you get as the answer you multiply it by 3. if you get the digits from te number that you multiplied then you know that number is a triply number. from the number 10 to 99 there are ONLY 2 NUMBERS. I saw people only give 2 numbers online and i was like why does no one give all the triply but in reality there are only 2 triply numbers which are 2 digits. You can check for yourself if you dont believe me using the method above. Thank you! I hope it helped if it helped please give me a thumbs up!
We will find that the "triply" numbers are:
-15, 15, -24, 24.
How to find the "triply" numbers?
We know that these aer two-digit numbers, so we can write them as:
a*10 + b
Where a and b are single-digit numbers.
A "triply" number is equal to 3 times the product of its digits, then we must have:
a*10 + b = 3*(a*b)
Moving all to one side, we have:
10a + b + 3ab = 0
So a "triply" number must meet the above criteria.
Now, the values that can take b are all the single-digit values {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
So now we need to evaluate b and find the possible vales of a.
if b = 0, then:
10*a + 0 - 3*a*0 = 0
10*a = 0
Then a = 0, but this will not give a 2-digit number.
if b = 1 then:
10*a + 1 - 3*a*1 = 0
10*a - 3a = -1
7*a = -1
a = -1/7
This is not a single-digit number.
if b = 2
10*a + 2 - 3*2*a = 0
4*a = -2
a = -2/4
This is not a single-digit number.
if b = 3
10*a + 3 - 3*3*a = 0
a = -3
a should be positive.
if b = 4 we have:
10a + 4 - 12a = 0
-2a = -4
a = -4/-2 = 2
So this gives the number 24.
if b = 5 we have
10a + 5 - 15a = 0
-5a = -5
a = -5/-5 = 1
So this gives the number 15
if b = 6
10a + 6 - 18a = 0
-8a = -6
a = -6/-8
This is not a single-digit.
if b = 7
10a + 7 -21a = 0
-11a = -7
a = -7/-11
At this point we can see that for larger values of a, we will not get more tripply numbers.
So the only "triply" numbers are: 15 and 24 (and their opposites, -15 and -24).
If you want to learn more about evaluating equations, you can read:
https://brainly.com/question/4344214