Question

A worker is installing blue and white square tiles in a kitchen. Blue tiles have different lengths than white tiles. A row of 8 blue tiles and 16 white tiles has a length of 39 inches. A row of 40 blue tiles and 8 white tiles has a length of 42 inches. Write a system of equations that represents in inches the relationship between the length of a blue tile and the length of a white tile.

Answer 1

8x+16y = 39 and 40x+8y = 42 are the system of equations that represents in inches the relationship between the length of a blue tile and the length of a white tile.

Explanation:

Let 'x' be the inches of a blue tile.

Let 'y' be the inches of a white tile.

8x+16y = 39 -------(1)

40x+8y = 42 -------(2)

Multiply eqn(2) by 2 and subtract it from eqn(1)

8x+16y = 39

(-) 80x+16y = 84

-72x = -45

⇒ x = -45/-72

⇒ x = 5/8

∴ Blue tile is 5/8 inches.

substitute x=5/8 in eqn(1)

⇒ 8(5/8) + 16y = 39

⇒ 16y = 39-5

⇒ y =34/16

⇒ y = 17/8

∴ White tile is 17/8 inches.