Need help with difficult physics problems

A boy on a 1.9 kg skateboard initially at rest
tosses a(n) 8.0 kg jug of water in the forward
direction.
If the jug has a speed of 2.9 m/s relative to
the ground and the boy and skateboard move
in the opposite direction at 0.57 m/s, find the
boy’s mass.
Answer in units of kg
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A 8.7 g bullet is stopped in a block of wood
(mw = 7.9 kg). The speed of the bullet-
plus-wood combination immediately after the
collision is 0.51 m/s.
What was the original speed of the bullet?
Answer in units of m/s
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A grocery shopper tosses a(n) 9.4 kg bag of
rice into a stationary 17.7 kg grocery cart.
The bag hits the cart with a horizontal speed
of 7.0 m/s toward the front of the cart.
What is the final speed of the cart and bag?
Answer in units of m/s

(1) total initial momentum = total final momentum
total Initial momentum = 0
total final momentum = (m_jug)(v_jug) + (m_boy+m_board)(v_board)
= (8kg)(2.9m/s) + (m_boy + 1.9kg)(−0.57m/s)

initial = final
0 = (8kg)(2.9m/s) + (m_boy + 1.9kg)(−0.57m/s)
Use basic algebra to solve for "m_boy"

(2) total initial momentum = total final momentum
total initial momentum = (m_bullet)(v_bullet_initial) = (0.0087kg)(v_bullet_initial)
total final momentum = (m_bullet + m_wood)(v_final) = (0.0087kg + 7.9kg)(0.51m/s) = (7.9087kg)(0.51m/s)

initial = final
(0.0087kg)(v_bullet_initial) = (7.9087kg)(0.51m/s)
Use basic algebra to solve for "v_bullet_initial"

(3) total initial momentum = total final momentum (do you see a theme here?)
total initial momentum = (m_bag)(v_bag_initial) = (9.4kg)(7.0m/s)
total final momentum = (m_bag+m_cart)(v_final) = (9.4kg+17.7kg)(v_final) = (27.1kg)(v_final)

initial = final
(9.4kg)(7.0m/s) = (27.1kg)(v_final)
Use basic algebra to solve for "v_final".