SOLUTION: 1.Half of an integer exceeds one-third of the next integer by unity. Find the integer. 2. The denominator of a fraction is 2 more than the numerator if 1 is added to both,the fr

Algebra ->  College  -> Linear Algebra -> SOLUTION: 1.Half of an integer exceeds one-third of the next integer by unity. Find the integer. 2. The denominator of a fraction is 2 more than the numerator if 1 is added to both,the fr      Log On


   

Question 1129626: 1.Half of an integer exceeds one-third of the next integer by unity. Find the integer.
2. The denominator of a fraction is 2 more than the numerator if 1 is added to both,the fraction is reduced to to 4/5 find the fraction.
3.divide 50 into two parts such that if 6is subtracted from one part and 12is added to the second part , we get the same number.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1.Half of an integer exceeds one-third of the next integer by unity. Find the integer.
1%2F2a = 1%2F3(a+1) + 1
multiply by 6, cancel the denominators
3a = 2(a+1) + 6
3a = 2a + 2 + 6
3a - 2a = 8
a = 8
Check this in the given statement
:
2. The denominator of a fraction is 2 more than the numerator
n%2F%28%28n%2B2%29%29
if 1 is added to both, the fraction is reduced to to 4/5 find the fraction.
%28n%2B1%29%2F%28%28n%2B2%29%2B1%29 = 4%2F5
find the fraction.
%28%28n%2B1%29%29%2F%28%28n%2B3%29%29 = 4%2F5
cross multiply
5(n+1) = 4(n+3)
5n + 5 = 4n + 12
5n - 4n = 12 - 5
n = 7
7%2F9 is the fraction
Check
Add 1 to both and you get 8%2F10 which reduces to 4%2F5
:
3.divide 50 into two parts
a + b = 50
such that if 6 is subtracted from one part and 12 is added to the second part, we get the same number.
a - 6 = b + 12
a - b = 12 + 6
a - b = 18
Use elimination on these two equations
a + b = 50
a - b = 18
------------addition eliminates b, find a
2a + 0 = 68
a = 68/2
a = 34
then obviously,
b = 16
Check see if this flies in the statement
"if 6 is subtracted from one part and 12 is added to the second part, we get the same number."
34 - 6 = 16 + 12