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If Kevin gives Diana $16, he will have the same amount of money as her. If Diana gives Kelvin $20, the amount of money she has will be 10% of his. How much money has each of them

Sagot :

Let call the amount Kevin has x and the amount Diana has y.

The equations describing this situation are

[tex]x-16=y[/tex][tex]y-20=0.1x[/tex]

Let us now solve the system.

The first equation gives us

[tex]x=y+16[/tex]

putting this into the second equation gives us

[tex]y-20=0.1(y+16)[/tex]

which simplifies to

[tex]y-20=0.1y+1.6[/tex]

Combing terms gives us

[tex]0.9y=21.6[/tex]

and dividing both sides by 0.9 gives us

[tex]y=24[/tex]

And now we solve for x.

[tex]x=16+24[/tex]

x = 40 and y =16

which is our answer!

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