The oldest son will get $370, the middle will get $220 and the youngest will get $185.
Step-by-step explanation:
Given,
Total amount to be split = $775
Let,
Oldest son's share = x
Middle son's share = y
Youngest son's share = z
According to given statement;
x+y+z=775 Eqn 1
the oldest gets twice as much as the youngest
x = 2z Eqn 2
the middle son gets $35 more than the youngest
y = z+35 Eqn 3
Putting value of x and y from Eqn 2 and 3 in Eqn 1
[tex]2z+(z+35)+z=775\\2z+z+35+z=775\\4z=775-35\\4z=740\\[/tex]
Dividing both sides by 4
[tex]\frac{4z}{4}=\frac{740}{4}\\z=185[/tex]
Putting z=185 in Eqn 2
[tex]x=2(185)\\x=370[/tex]
Putting z=185 in Eqn 3
[tex]y=185+35\\y=220[/tex]
The oldest son will get $370, the middle will get $220 and the youngest will get $185.
Keywords: linear equation, substitution method
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