Question

Ms. Ashley has less than 100 pieces of candy.

If she makes groups of 2 pieces, she will have 1 piece left over.
If she makes groups of 3 pieces, she will have 1 piece left over.
If she makes groups of 3 pieces, she will have 1 piece left over.
If she makes groups of 4 pieces, she will have 1 piece left over.
If she makes groups of 5 pieces, she will have 0 pieces left over.

How many pieces of candy could she have? Find all solutions.
Please help me on this! I really need help.

Answer 1

25 ,55 85

Explanation:

In order to have 0 left making 5 groups,the number should end on 0 or 5

But in order to have 1 left in gruups of 2 and 4 it should be odd number so the number must end in 5

But the the two numbers after subracting 1 must add a multiple of 3

15-1=14 1+4=5 (no multiple of 3)

25-1 = 24 2+4=6 (yes)

35-1=34 3+4=7(no)

45-1=44 4+4=8(no)

55-1 = 45 4+5 =9 (yes)

65-1=64 6 +4 =10(no)

75-1=74 7+4=11 (no)

85-1=84 8+4 = 12 (yes)

95-1=94 9+4=13 (no)

Answer 2

85-25

Explanation:

85:2=42 left1

85:3=28 left 1

85:4=21left1

85:5=17 left 0

25:2=12 left 1

25:3=8 left 1

25:4=6 left 1

25:5=5 left 0