Question

Irene is making a patchwork quilt. She has completed a rectangular section that is 2 patches long and 3 patches wide. Each week, she plans to make the quilt one patch longer and 2 patches wider. The total number of patches in the quilt after x weeks is given by the product: (___) • (___) The total number of patches in the quilt after x weeks is given by the product: (___) • (___) What goes in the blanks?

Answer 1

The total number of patches in the quilt after x weeks is given by the product:

length times width

The total number of patches in the quilt after weeks is given by the product:

2+x times 3+2x

Answer 2

`(2+x).(3+2x)` is the total number of patches in the quilt after 'x ' weeks.

Explanation:

Given:

Irene has completed rectangular section which is 2 patches long and 3 patches wide.

To find:

Formula for number of patches after x weeks.

Solution:

Total number of patches in the first week = 2 + 2 +2 = 6

OR

we can simply calculate the number of patches by multiplying 2 with 3.

Given that every week,

The quilt will be one patch longer and 2 patches wider.

After
`x` number of weeks,

The quilt will be
`x * 1` patches longer and
`x * 2` patches wider.

OR

The quilt will be
`x` patches longer and
`2x` patches wider.

Initially, it was 2 patches long and 3 patches wide.

So, after x weeks:

The quilt will be
`2+x` patches longer and
`3+2x` patches wider.

And total number of patches, after x weeks will be given as:

`(2+x).(3+2x)`