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 remainin

Question

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*

0

Answers ( No )

    0
    2021-09-09T02:29:43+00:00

    Answer:

    15 problems were assigned

    Explanation:

    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.

    0
    2021-09-09T02:29:47+00:00

    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

Leave an answer

Browse
Browse