Karen has $30, Rafael has $75 and Shen has $25.
Step-by-step explanation:
Given,
Total amount they have = $130
Let,
Amount of Karen = x
Amount of Rafael = y
Amount of Shen = z
According to given statement;
x+y+z=130 Eqn 1
Shen has $5 less than what Karen have.
z = x-5 Eqn 2
Rafael has 3 times what Shen has;
y = 3z Eqn 3
Putting value of z from Eqn 2 in Eqn 3
[tex]y=3(x-5)\\y=3x-15\ \ \ \ Eqn\ 4[/tex]
Putting value of y and z from Eqn 4 and 2 in Eqn 1
[tex]x+(3x-15)+(x-5)=130\\x+3x-15+x-5=130\\5x-20=130\\5x=130+20\\5x=150[/tex]
Dividing both sides by 5
[tex]\frac{5x}{5}=\frac{150}{5}\\x=30[/tex]
Putting x = 30 in Eqn 2
[tex]z=30-5\\z=25[/tex]
Putting z=25 in Eqn 3
[tex]y=3(25)\\y=75[/tex]
Karen has $30, Rafael has $75 and Shen has $25.
Keywords: linear equations, substitution method
Learn more about linear equations at:
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