SOLUTION: The difference between two numbers is 20. Five times the smaller is the same as 4 less than twice larger. Find the numbers

Question 516749: The difference between two numbers is 20. Five times the smaller is the same as 4 less than twice larger. Find the numbers
Found 2 solutions by mananth, oberobic:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
bigger number -----x
smaller nuber -----y
x-y =20..........1
5y=2x-4
5y-2x=-4.........2
solve for x & y
1 x -1 y = 20 .............1
-2 x + 5 y = -4 .............2
Eliminate y
multiply (1)by 5
Multiply (2) by 1
5 x -5 y = 100
-2 x 5 y = -4
Add the two equations
3 x = 96
/ 3
x = 32
plug value of x in (1)
1 x + -1 y = 20
32 + -1 y = 20
-1 y = 20
-1 y = -12
y = 12

Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Two numbers: x & y.
.
x - y = 20
so
x = y+20
.
5x = 2y-4
.
substitute
.
5(y+20) = 2y-4
5y + 100 = 2y -4
3y + 100 = -4
3y = -104
y = -104/3
.
x-y = 20
x-(-104/3) = 20
x + 104/3 = 20
x = 20 - 104/3
x = 60/3 -104/3
x = -44/3
.
check to see if this works
.
5x = 2y-4
5(-44/3) = -220/3
2y-4 = 2(-104/3) -4
2y-4 = -208/3 - 12/3 = -220/3
.
Answer: The numbers are -104/3 and -44/3.
.
Done.
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