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Eric is twice as old as his brother Lucas. If 4 is subtracted from Eric's age and 4 is added to Lucas' age, their ages will be equal. What are the boys' ages now?

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Jers15id
Lets represent:
x=Eric's age
y=Lucas's Age

The first equation:
x=2y

The second equation:
x-4=y+4
Substitute
2y-4=y+4
Subtract y to both sides
y-4=4
Add 4 to both sides
y=8

Therefore: Lucas's age is 8 while Eric's age is 16.

Hope this helps =)

Mlcparra16id
We let Lucas' age be x, this would make Eric's age 2x. 
From the second sentence we would have;
[tex]2x-4=x+4 \\ 2x-4-x=x+4-x \\ x-4=4 \\ x-4+4=4+4 \\ x=8[/tex]

Therefore Lucas' age is 8 and Eric's is 2*8 or 16.