Missy uses 1 hexagonal, 2 rectangular, and 4 triangular pieces of fabric to make 1 bug design for a quilt. if she uses 70 pieces in all to make bug designs, how many of each shape does she use?

According to the problem's info, we have:
(1 + 2 + 4)pieces of fabric = 1bug
(7)pieces of fabric = 1bug
so we know for each bug Missy uses 7 pieces of fabric (of different shapes).
Then, if she uses 70 pieces (7*10) of fabric, those are 10 bugs(1*10) built.
so we have to multiply by 10 the amount of pieces used in one bug:
hexagonal = 1*10 = 10
rectangular = 2*10 = 20
triangular = 4*10 = 40
which give us 70 pieces total.