SOLUTION: If one-half of one integer is subtracted from three-fifths of the next consecutive integer, the difference is 3. What are the two integers? I wrote for following expressions:

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: If one-half of one integer is subtracted from three-fifths of the next consecutive integer, the difference is 3. What are the two integers? I wrote for following expressions:       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 59256: If one-half of one integer is subtracted from three-fifths of the next consecutive integer, the difference is 3. What are the two integers?
I wrote for following expressions:
a =
b = a+6
c = 3(a+b)-4
I am unable to solve for the three angles. Your help is appreaciated.
Thank you.

Found 2 solutions by armidano, josmiceli:
Answer by armidano(1) About Me  (Show Source):
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You have 3 unknowns
That means you need 3 equations, or you can't solve.
The one you're missing is:
a + b + c = 180 That's true of all triangles
[1]b+=+a+%2B+6
[2]c+=+3%2A%28a+%2B+b%29+-+4
[3]a+%2B+b+%2B+c+=+180
expand [2]
c+=+3a+%2B+3b+-+4
subtract c from both sides
[4]3a+%2B+3b+-+c+-+4+=+0
add 4 to both sides
3a+%2B+3b+-+c+=+4
multiply both sides of [3] by 3
3a+%2B+3b+%2B+3c+=+540
subtract one from the other
4c+=+536
c+=+134
substitute in [4]
3a+%2B+3b+-+134+-4+=+0
[5]3a+%2B+3b+=+138
[1]b+=+a+%2B+6
a+-+b+=+-6
muiltiply both sides by 3
3a+-+3b+=+-18
add to [5]
6a+=+120
a+=+20
[3]a+%2B+b+%2B+c+=+180
20+%2B+b+%2B+134+=+180
b+%2B+154+=+180
b+=+26
check
[1]b+=+a+%2B+6
26+=+20+%2B+6
26+=+26
[2]c+=+3%2A%28a+%2B+b%29+-+4
134+=+3%2A%2820+%2B+26%29+-+4
134+=+3%2A46+-+4
134+=+138+-+4
134+=+134
OK
so,
a = 20 degrees
b = 26 degrees
c = 134 degrees