Answer:
Originally
The number of coins in the first box was [tex]67\ coins[/tex]
The number of coins in the second box was [tex]83\ coins[/tex]
Finally
The number of coins in the first box is [tex]50\ coins[/tex]
The number of coins in the second box is [tex]100\ coins[/tex]
Step-by-step explanation:
Let
x-----> number of coins in the first box originally
y-----> number of coins in the second box originally
we know that
[tex]x+y=150[/tex]
[tex]x=150-y[/tex] -----> equation A
[tex](y+17)=2(x-17)[/tex] -----> equation B
substitute equation A in equation B
[tex]y+17=2x-34[/tex]
[tex]y+17=2(150-y)-34[/tex]
[tex]y+17=300-2y-34[/tex]
[tex]y+2y=300-34-17[/tex]
[tex]3y=249[/tex]
[tex]y=83\ coins[/tex]
Find the value of x
[tex]x=150-83=67\ coins[/tex]
therefore
Originally
The number of coins in the first box was [tex]67\ coins[/tex]
The number of coins in the second box was [tex]83\ coins[/tex]
Finally
The number of coins in the first box is [tex](67-17)=50\ coins[/tex]
The number of coins in the second box is [tex](83+17)=100\ coins[/tex]
