Two days ago, neil was assigned a set of problems to solve. today he solved the final three. yesterday he solved half of those then remaining plus half a problem. the first day he solved half of those assigned plus half a problem. how many problems were in the assigned set. *show work*

x = number of problems

1st day : 1/2x +.5

remaining problems

x-(1/2x +.5)

2nd day: 1/2(x- (1/2x +.5))+.5

day 3 : 3

in 3 days he solved all the problems or x

x = 1/2 x +.5 + 1/2(x- (1/2x +.5))+.5 +3

distribute

x = 1/2 x +.5 +1/2 (x-1/2 x -.5) +.5 +3

combine like terms

x = 1/2 x +.5 +.5 +3 +1/2 (+1/2 x-.5)

distribute

x =1/2 x +4 +1/4 x -1/4

multiply each side by 4 to get rid of the fractions

4x = 4 (1/2 x +4 +1/4 x -1/4)

distribute

4x = 2x +16 +x-1

combine like terms

4x = 3x +15

subtract 3x from each side

x = 15

There were 15 problems assigned

15 problems were assigned

Let n represent the original number of problems.

At the end of Day 1, the number of remaining problems was (n/2 -1/2).

At the end of Day 2, the number of remaining problems was ...

... (n/2 -1/2)/2 -1/2 = 3

Simplifying, this is ...

... n/4 -1/4 -1/2 = 3 . . . . . eliminate parentheses

... n/4 = 3 3/4 = 15/4 . . . add 3/4, convert mixed number to improper fraction

... n = 15 . . . . . . . . . . . . . multiply by 4

There were 15 problems in the set.

15 batches are the most you can make

step-by-step explanation: