let

x = the amount of money Tommy has

y = the amount of money Emma has

z = the amount of money Shannon has

Tommy has twice as much money as Emma:

x = 2y

Shannon has $10 less than Emma:

z = y - 10

Together they have $70:

x + y + z = 70

by solving the system of equations:

x = 2y

z = y - 10

x + y + z = 70

we find:

x = $40

y = $20

z = $10

click here to see the step by step solution of the system of equations:

Tommy has $40, Emma has $20 and Shannon has $10.