Question 149189
1.) One number is 3 more than the other. Their sum is 7. Find the numbers. 
y=x+3, x+y=7 then x+x=3=7 then 2x=4 then x=2 and y=5

2.) The denominator of a fraction is twice the numerator. If the sum of the
terms is 3, what is the fraction? 
fraction is x/2x  x+2x=3x=3 then x=1 and fraction is 1/2

3.) The sum of two numbers is 165 and their difference is 29. Find the
numbers. 
x+y=165
x-y=29
adding

2x=194
x=97 and y=68

4.) If the numerator of a certain fraction is increased by 6 and its 
denominator is decreased by 5, the resulting fraction is equal to 3/4.
If the reciprocal of the original fraction is decreased by 1, the 
resulting fraction is 16/9. Find the original fraction.

fraction is x/y

(x+6)/(y-5)=3/4
(y/x)-1=16/9

then

4(x+6)=3(y-5)
y/x=25/9

4x+24=3y-15
9y=25x

4x-3y=-39
-25x+9y=0

12x-9y=-117
-25x+9y=0

adding


-13x=-117
x=9
y=25

so fraction is 9/25