Question

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Answer 1

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

$y=3(x-5)\\y=3x-15\ \ \ \ Eqn\ 4$

Putting value of y and z from Eqn 4 and 2 in Eqn 1

$x+(3x-15)+(x-5)=130\\x+3x-15+x-5=130\\5x-20=130\\5x=130+20\\5x=150$

Dividing both sides by 5

$\frac{5x}{5}=\frac{150}{5}\\x=30$

Putting x = 30 in Eqn 2

$z=30-5\\z=25$

Putting z=25 in Eqn 3

$y=3(25)\\y=75$

Karen has $30, Rafael has $75 and Shen has $25.

Keywords: linear equations, substitution method

Learn more about linear equations at:

• brainly.com/question/13063819
• brainly.com/question/13219835

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