Question

the sum of two different numbers is 40 . if the smaller number is divided by 4 and the larger number by 12 the sum of the quotients is 6.find the larger number

Answer 1

Let x represent the smaller number, and y the larger. You have two equations in 2 unknowns. Sentence one produces
1) x + y = 40
Sentence two produces
2) (x/4) + (y/12) = 6
Now you have to work to eliminate one variable.
If you multiply the entire equation 2 by -12
-12[(x/4) + (y/12) = 6]
you obtain
-3x - y = -72 then add it to number 1)
x + y = 40
You obtain
-2x = - 32, thus dividing by -2 you get x, then sub it back into an original equation and solve for y