SOLUTION: please help me solve this equation: one third of a number added to one quarter of a smaller number equals 18. the difference between the two numbers is 26. what are the two numbers

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Question 904769: please help me solve this equation: one third of a number added to one quarter of a smaller number equals 18. the difference between the two numbers is 26. what are the two numbers???
Found 2 solutions by josgarithmetic, mananth:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The two numbers are x and y. Assume y%3Ex.

y%2F3%2Bx%2F4=18 and y-x=26.

That is what the description means. Now just solve the system.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let the numbers be x & y
I condition
(1/3)x+(1/4)y =18
II condition
x-y 26
(1/3)x+(1/4)y =18
LCM of the denominator is 12
multiply equation by 12
4x+3y=216
4 x + 3 y = 216 .............1

1 x -1 y = 26 .............2
Eliminate y
multiply (1)by 1
Multiply (2) by 3
4 x 3 y = 216
3 x -3 y = 78
Add the two equations
7 x = 294
/ 7
x = 42
plug value of x in (1)
4 x + 3 y = 216
168 + 3 y = 216
3 y = 216 -168
3 y = 48
y = 16