Hello there. To solve this question, we'll have to set some relations between the weights of the carts for Joseph, Anna and Heather and find their values using one of the given value.
First, knowing Joseph's cart weighs 12 pounds less than Heather's, say J is Joseph's cart weight and H is Heather's cart weight.
With the information, we have that:
J = H - 12
Now, knowing Anna's cart weight is half as much as Heather's, we have the following relation:
A = H + 1/2 * H = 3/2 * H
Now, to find a direct relation between Anna's cart weight and Joseph's cart weight, we multiply the first equation by 3/2:
3/2 J = 3/2 H - 12
Where 3/2 H = A, therefore
3/2J = A - 12
Multiply both sides by a factor of 2/3
J = 2/3 A - 8
Plugging in A = 34, we finally get:
J = 2/3 * 34 - 8
J = 22.67 - 8 = 14.67 pounds.