SOLUTION: Find the two digit number. The sum of the digits is 8. The product of the digits is 12. The number is between 30 and 90.

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: Find the two digit number. The sum of the digits is 8. The product of the digits is 12. The number is between 30 and 90.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 525789: Find the two digit number. The sum of the digits is 8. The product of the digits is 12. The number is between 30 and 90.
Found 2 solutions by solver91311, josmiceli:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent one of the digits, and represent the other. Then:



Which is to say



Then



Substituting:



Solve the quadratic for . One root will be one of the digits, the other root will be the other digit. The restriction on the output tells you which order to put them in.

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the units digit n
Call the tens digit m
given:
(1) +m+%2B+n+=+8+
(2) +m%2An+=+12+
------------
(2) +n+=+12%2Fm+
Substitute this into (1)
(1) +m+%2B+12%2Fm+=+8+
(1) +m%5E2+%2B+12+=+8m+
(1) +m%5E2+-+8m+%2B+12+=+0+
use the quadratic formula
m+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+-8+
+c+=+12+
m+=+%28-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%2A1%2A12+%29%29%2F%282%2A1%29+
m+=+%28+8+%2B-+sqrt%28+64+-+48+%29%29+%2F+2+
m+=+%28+8+%2B-+sqrt%28+16+%29%29+%2F+2+
-----------------------
+m+=+%28+8+%2B+4+%29+%2F+2+
+m+=+6+
and, also
+m+=+%28+8+-+4+%29+%2F+2+
+m+=+2+
----------
If +m+=+6+
(1) +m+%2B+n+=+8+
(1) +n+=+2+
The number is 62, which is between 30 and 90
and is the correct answer
----------
If +m+=+2+
(1) +2+%2B+n+=+8+
(1) +n+=+6+
The number is 26, which is less than 30