separate 40 into two parts so that 3/5 of the larger part added to 1/2 of the smaller part is 29

Question

Please Help. Algebra ll

Answer 1

Let x represent bigger number

let y represent smaller number

x+y=40..equation 1

3/5x+1/2y=29..equation 2

 

because equation 2 is in fraction I will use the common factor of 10(2*5) to eliminate fractions by multiplying 

10(3/5x+1/2y=29)=

6x+5y=290

 

x+y=40

6x+5y=290

 

now use elimination method

to solve for x, we will make the y equal in both equations 

-5(x+y=40)=

-5x-5y=-200

 6x+5y=290....add equations 

=========

 x      =90

 

now substitute value of x to get y using:

x+y=40

 90+y=40

-90    =-90...add

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         y=-50

 

answers x=90, y=-50

 

lets check

3/5(90)+1/2(-50)=29

54+(-25)=29

54-25=29..yes