Question

At the end of April, Mandy told Bill that she has read 16 books this year and reads 2 books each month. Bill wants to catch up to Mandy. He tracks his book reading with a table on his door. Using his table below, what month will Bill have read the same amount of books as Mandy?

Month Books
May 4
June 8
July 12

Answer 1

What is the situation in May?

Bill has read 4 books (from the table) and Mandy has read 16 +2 books, which is 18 in total

In May, Mandy read a lot more books than Bill.



What is the situation in June?

Bill has read 4 +8=12 books (from the table; I added up May and June books) and Mandy has read 16 +2 +2books, which is 20 in total

In June, Mandy read a lot more books than Bill.

What is the situation in July?

Bill has read 12+12=24 books (from the table; I added up May and June and July books) and Mandy has read 16 +2 +2+2books, which is 22 in total

So at the end of June, Bill will have read more books than Mandy!
So he probably doesn't need to read the last two books.

And the answer is: July.

Answer 2

we know that

In an Arithmetic Sequence the difference between one term and the next is a constant

`an=a1+d*(n-1)`

where

a1 is the first term

d is the common difference between terms

n is the number of months (in this problem)

case a) Mandy

`a1=16 books`

`d=2`

`an=16+2*(n-1)` ------> equation
`1`

in this equation the first month is April

case b) Bill

`a1=4 books`

`d=4`

`an=4+4*(n-1)` -------> equation
`2`

In this equation the first month is May

With the equation
`1` and the equation
`2`

calculate the attached table

therefore

the answer is

December