Question

suppose that we agree to pay you 8cents for every problem in this chapter that you solve correctly and fine you 5cents for every problem done incorrectly, if the end of 26 problems we do not you each other any money, how many problems did you do?

Answer 1

8x = 5(26-x)
solve for x

Answer 2

a thief steals a number of rare plants from a nursery, on the way out the thief meets three security guards, one after another, to each security guard, the thief is forced to give one-half the plants that he still has, plus 2 more, the theif is left with one plant, how many plants were originally stolen?
so this is how i set it up:
.5(3x+2)=1
and i get zero which is wrong

Answer 3

Your equation makes no sense to me

Look at it this way :

suppose he stole x plants
after passing the first guard he has left:
.5x - 2
after passing the second guard he has left:
.5(.5x-2)-2
after passing the third guard he has left:
.5[.5(.5x-2)-2] - 2

but this equals 1, so

.5[.5(.5x-2)-2] - 2 = 1

solving this I got x=36

check:
to the first guard he gives 18+2, leaving him with 16
to the second guard he gives 8+2, leaving him with 6
to the third guard he gives 3+2, leaving with with 1
Q.E.D.