Question

Thi is designing a patio with bricks that are 8 inches and 12 inches in length. Thi wants to use alternating rows of 8-inch and 12-inch bricks. If she uses up to 9 bricks in a row What Are some Combinations of 8-inch and 12-inch bricks that Will Produce rows of equal Length?

Answer 1

(3 , 2) is the only possible combination of 8-inch and 12-inch bricks that Will Produce rows of equal Length.

Solution-

Thi is designing a patio with bricks that are 8 inches and 12 inches in length. She wants to use both the bricks.

As she decides to use alternating rows of both the brick with same length of patio,

So we can calculate the number of bricks needed by calculate the LCM,

LCM of 8 and 12 is 24.

So length of the rows of the patio must be a multiple of 24 in order to make all the length of the rows of the patio same.

Now, we have to calculate the number of bricks of each categories,

so number of bricks of 8 inches (if the length is 24 inches) =
`(24)/(8) =3`

and number of bricks of 12 inches (if the length is 24 inches) =
`(24)/(12) =2`

Hence, the number of 8 inches bricks will be a multiple of 3 and the number of 12 inches bricks will be a multiple of 2.

Then the possible combinations of 8-inch and 12-inch bricks that produce rows of equal length of patio are (3,2),(6,4),(9,6),(12,8) and so on.

It is also given that she uses up to 9 bricks in a row,

So (3,2) is the only possible combination. ( ∵ As all the other combinations need more than 9 bricks)