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

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) (Show Source): You can put this solution on YOUR website!
The two numbers are x and y. Assume .

and .

That is what the description means. Now just solve the system.
Answer by mananth(16946) (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

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