Question

Bella is planning to write in a journal. Some pages will have one journal entry on them, and other pages will have two journal entries on them. If Bella wants to make 10 entries, how many different ways can she write them in her journal?

Answer 1

Answer: 6 ways

Explanation:

Given : Bella is planning to write in a journal.

Some pages will have one journal entry on them, and other pages will have two journal entries on them.

Total required entries to make = 10

We can write 10 =10(1)+0

i.e. she can write one entry one journal entry on each page. → Way 1

10=8(1)+2(1)

i.e. she can write one entry one journal entry per page for 8 pages and 2 journal entries on one page .→ Way 2

10=6+4 = 6(1)+2(2)

i.e. she can write one entry one journal entry per page for 6 pages and 2 journal entries on 2 pages . → Way 3

10=4+6 = 4(1)+2(3)

i.e. she can write one entry one journal entry per page for 4 pages and 2 journal entries on 3 pages .→ Way 4

10=2+8 = 2(1)+2(4)

i.e. she can write one entry one journal entry per page for 2 pages and 2 journal entries on 4 pages .→ Way 5

10=0+10= 0+ 2(5)

i.e. she can write 2 journal entries on 5 pages . → Way 6

Hence, the total number of ways she can write them in her journal = 6

Answer 2

The correct answer is:

6 ways.

Explanation:

She wants a total of 10 journal entries.

She can write each entry on a separate page, for 10 pages used.
She can write 8 entries on separate pages and 2 entries on 1 page, for 9 pages used.
She can write 6 entries on separate pages and 2 entries each on 2 separate pages, for 8 pages used.
She can write 4 entries on separate pages and 2 entries each on 3 separate pages, for 7 pages used.
She can write 2 entries on separate pages and 2 entries each on 4 separate pages, for 6 pages used.
She can write 2 entries each on 5 separate pages, for 5 pages used.