Answer: 57 ; 72
Explanation:
Given information
2/3 of a number is 2 more than (1/2) of another number
Sum = 129
Set variables
Let x be the first number
Let y be the other number
Set system of equations
[tex]1)~\dfrac{2}{3} x=\dfrac{1}{2} y+2[/tex]
[tex]2)~x + y=129[/tex]
Eliminate fractions in the 1) equation
[tex]\dfrac{2}{3} x\times6=\dfrac{1}{2} y\times6+2\times6[/tex]
[tex]4x=3y+12[/tex]
Move x and y onto the same side
[tex]4x-3y=12[/tex]
Current System
[tex]1)~4x-3y=12[/tex]
[tex]2)~x + y=129[/tex]
Multiply 3 on both sides in 2) equation
[tex]x\times3 + y\times3=129\times3[/tex]
[tex]3x+3y=387[/tex]
Current System
[tex]1)~4x-3y=12[/tex]
[tex]2)~3x+3y=387[/tex]
Add 1) equation and 2) equation together
[tex](4x - 3y)+(3x+3y)=(12)+(387)[/tex]
Expand parenthesis and combine like terms
[tex]4x - 3y + 3x + 3y = 12 + 387[/tex]
[tex]4x + 3x - 3y + 3y=399[/tex]
[tex]7x=399[/tex]
Divide 7 on both sides
[tex]7x\div7=399\div7[/tex]
[tex]\Large\boxed{x=57}[/tex]
Substitute the x value into one of the equations to find the y value
x + y = 129
(57) + y = 129
y = 129 - 57
[tex]\Large\boxed{y=72}[/tex]
Hope this helps!! :)
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