Which explanation best describes how to solve this problem?

heidi was making decorations for the holiday sale. she sold 22 decorations. then, during her break, she made 17 more. she sold another 16. now heidi has 12 decorations left. how many decorations did heidi have to begin with?

a.
guess and test.
guess that heidi had 50 decorations to begin with. subtract the number she sold, add the number she made, then subtract the second amount she sold. this gives 29.
that is 17 more than 12.
add 17 to your guess.
heidi had 67 decorations to begin with.

b.
draw a diagram.
draw 22 decorations. add another 17 decorations and then add another 16. cross out the 12 decorations that heidi has left over to figure out that heidi started with 43 decorations to begin with.

c.
translate into an equation.
22 + 17 – 16 + 12 = b
heidi had 35 decorations to begin with.

d.
work backward.
start with the number of decorations that were sold (16 and 22). add those two amounts together (38).
take away decorations that she made during her break (17) because she didn't have these at the start. then add the 12 she still has.
heidi had 33 decorations to begin with.