Answer :
[tex]x-\ number \ of\ Michelle's\ berries\\
y-\ number\ of \ Joe's\ berries\\
z-number\ of \ Ian's\ berries\\\\
z=5x\\
y=7x\\
x+y+z=208\\\\
x+5x+7x=208\\\\
13x=208\ \ \ \ | divide\ by\ 13\\\\x=16\\\\
y=16*7=112\\\\
Joe\ picked\ 12\ berries.[/tex]
Ian =x
Michelle=y
Joe=z
5y=x
7y=z
so 5z=35y=7x
5z=7x
208=x+y+z
substitute
x and z to get
208=(5y)+y+(7y) or
208=13 y
divide both sides by 13
michelle picked 16
Joe picked 7 times than Michelle so
16 times 7=112
Michelle=y
Joe=z
5y=x
7y=z
so 5z=35y=7x
5z=7x
208=x+y+z
substitute
x and z to get
208=(5y)+y+(7y) or
208=13 y
divide both sides by 13
michelle picked 16
Joe picked 7 times than Michelle so
16 times 7=112