SOLUTION: This is my problem: A two-digit counting number has a value that is 8 times the sum of its digits. If 6 times the units' digit is 5 more than the tens' digit, what is the number? M

Algebra.Com
Question 1097847: This is my problem: A two-digit counting number has a value that is 8 times the sum of its digits. If 6 times the units' digit is 5 more than the tens' digit, what is the number? My math book has not given me an example of this variation of kind of problem, and I can't find one on YouTube. Can you help me learn to solve this? Walk me through the different steps? Thank you for your time!
Found 3 solutions by ikleyn, greenestamps, MathTherapy:
Answer by ikleyn(52771)   (Show Source): You can put this solution on YOUR website!
.
Let T be the tens digit and U be the ones digit.

Then your number N is N = 10*T + U.


First part of the condition gives you this equation:

10*T + U = 8*(T+U).    (1)


Second part of the condition gives you another equation:

6*U = T + 5.           (2)


Thus you have this system of two equations

10*T + U = 8*(T+U),    (1)
 6*U = T + 5.          (2)


which you can easily solve.


Since I do not want to deprive you this pleasure to solve it on your own, I leave the solution to you.

Happy solving ! !



Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

Learning how to solve this kind of problem using formal algebra is good training. However, equally valuable is being able to use logical reasoning to solve this kind of problem. Let's look at how we could solve this problem using logical analysis.

"A two-digit counting number has a value that is 8 times the sum of its digits."

Okay; there is no obvious clue there, at least that I can see.... So

"6 times the units' digit is 5 more than the tens' digit

Whoa!! If the units digit is very large, then 6 times it is going to be way more than 5 more than some single digit:
If the units digit is 1, then the tens digit would have to be 1 also (6*1 = 1+5).
If the units digit is 2, then the tens digit would have to be 7 (6*2 = 7+5).

Clearly if the units digit is any larger, the "tens digit" could not be a single digit.

So we only have two possibilities: the 2-digit number is either 11 or 72.

Only 72 satisfies the first condition; so 72 is the number we are looking for.

Studying mathematics is supposed to teach you to think; don't be afraid to exercise your brain by solving problems by thinking them through logically.
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
This is my problem: A two-digit counting number has a value that is 8 times the sum of its digits. If 6 times the units' digit is 5 more than the tens' digit, what is the number? My math book has not given me an example of this variation of kind of problem, and I can't find one on YouTube. Can you help me learn to solve this? Walk me through the different steps? Thank you for your time!
The only sentence you need in order to figure this out is this, "A two-digit counting number has a value that is 8 times the sum of its digits." Nothing else!!



Let the tens and units digits be T and U, respectively

Then the number is: 10T + U, and we get: 10T + U = 8(T + U)

10T + U = 8T + 8U

10T - 8T = 8U - U

2T = 7U <====== This means that T = 7, and U = 2, as these are the only 2 DIGITS that satisfy this equation.

Hence, the number is: . That's it!! 

RELATED QUESTIONS


A two digit counting number has a value of 8 times the sum of its digits. If 6 times the... (answered by nerdybill)

A two digit counting number has a value of 8 times the sum of its digits. If 6 times the... (answered by nerdybill)

A two-digit counting number has a value that is 1 greater than 8 times the sum of its... (answered by lwsshak3)

A two-digit counting number has a value that is 7 more than 6 times the sum of its... (answered by josgarithmetic)

A two digit counting number has a value that is 7 more than 6 times the sum of its... (answered by ankor@dixie-net.com)

A two-digit counting number has a value that is 7 times the sum of its digits.  If 5... (answered by ankor@dixie-net.com)

A two digit counting number has a value that is 4 times the sum of its digits. If 4 times  (answered by ankor@dixie-net.com)

A certain two-digit number has a value that is 2 more than 6 times the sum of its digits.  (answered by mananth,ankor@dixie-net.com)

a certain two digit number has a value that is 2 more than 6 times the sum of its digits.  (answered by ankor@dixie-net.com)