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?

10 hexagonal

20 rectangular

40 triangular

First add the 2+1+4=7

The divide 70 by 7 to get 10 the times each of the shapes by ten

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.