SOLUTION: Please help with this. Thanks Eric is 2 years younger than his brother Bill and 2 years older that his sister Beth. The sum of the 3 is 60 years. What is the age of each person?

Question 163736: Please help with this. Thanks
Eric is 2 years younger than his brother Bill and 2 years older that his sister Beth. The sum of the 3 is 60 years. What is the age of each person?
Found 2 solutions by ankor@dixie-net.com, gonzo:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!

Write an equation for each statement, put it in terms of E
:
Eric is 2 years younger than his brother Bill
E = Bi - 2
Bi = E + 2
:
and 2 years older that his sister Beth.
E = Be + 2
Be = E - 2
:
The sum of the 3 is 60 years.
E + Bi + Be = 60
:
What is the age of each person?
:
Substitute (E+2) for Bi and (E-2) for Be
E + (E+2) + E-2) = 60
2's cancel so you have:
3E = 60
:
E = 20, then Bi = 22, Be = 18
:
:

Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
Let x = Eric's age
Let y = Bill's age
Let z = Beth's age
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since Eric is 2 years younger than his brother Bill,
x = y-2
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since Eric is 2 years older than his sister Beth,
x = z+2
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since the sum of all their ages equals 60,
x + y + z = 60
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since y-2 and z+2 are both equal to x, then they are equal to each other.
y-2 = z+2
solving for y, we get
y = z+4
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we should be able to solve for z.
using the equation for the sum of their ages = 60, we have
x + y + z = 60
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since y = z+4, we can substitute in the equation to get
x + (z+4) + z = 60
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since x = z + 2, we can substitute in the original equation again to get
(z+2) + (z+4) + z = 60
this becomes
z+2+z+4+z = 60
which becomes
3z+6 = 60
which becomes
3z = 54
which becomes
z = 18
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since we know z, we can solve for x and for y.
x = z+2 = 18 + 2 = 20
y = z+4 = 18 + 4 = 22
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sum of their ages is 60
x + y + z = 60
20 + 22 + 18 = 60
60 = 60
sum equations are good.
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x = Eric's age = 20
y = Bill's age = 22
z = Beth's age = 18
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Eric is 2 years younger than Bill.
20 + 2 = 22
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Eric is 2 years older than Beth
20 - 2 = 18
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all formulas check out.
Eric is 20
Bill is 22
Beth is 18
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