Question

Marco is making Mosaic garden tools using red yellow and blue tiles. He has 45 red tiles, 90 blue tiles, and 75 yellow tiles. Each Stone must have the same number of each color tile. How many of each color tile will Marco use in each stone if the greatest number of stones he can make is 45?

Answer 1

Marco will use 3 red, 6 blue and 5 yellow tiles on each stones

Explanation:

Given, each stone must have same number of each colour tile

Then, calculating the highest common factors of the number HCF (45, 90, 75)

Factors of 45 = 3 × 3 × 5

Factors of 90 = 2 × 3 × 3 × 5

Factors of 75 = 3 × 5 × 5

Highest Common Factors (HCF) = 3 × 5 = 15

Dividing all three numbers by 15, we get

Red Tiles =
`(45)/(15)` = 3

Blue Tiles =
`(90)/(15)` = 6

Yellow Tiles =
`(75)/(15)` = 5

Therefore, Marco will use 3 red, 6 blue and 5 yellow tiles on each stones

Answer 2

Marco will use
`1` red tile,
`2` blue tiles and
`1(2)/(3)` yellow tiles in each stone.

Explanation:

Given:

Number of red tiles = 45

Number of blue tiles = 90

Number of yellow tiles = 75

Greatest number of stones that Marco can make = 45

To determine how many each color tile Marco will use in each stone.

Solution:

In order to determine the number of each color tile in each stone we need to divide total number of a particular tile by total number of stones. By doing this we can get the exact number of that color tile used in each stone.

Number of red tile in each stone

⇒
`\frac{\textrm{Total number of red tiles}}{\textrm{Total number of stones}}`

⇒
`(45)/(45)=1`

Number of blue tiles in each stone

⇒
`\frac{\textrm{Total number of blue tiles}}{\textrm{Total number of stones}}`

⇒
`(90)/(45)=2`

Number of yellow tile in each stone

⇒
`\frac{\textrm{Total number of yellow tiles}}{\textrm{Total number of stones}}`

⇒
`(75)/(45)`

⇒
`(5)/(3)` [Reducing to simpler fraction by dividing both numbers by their GCF=15]

⇒
`1(2)/(3)` [Converting improper fraction to mixed number]

∴ Marco will use
`1` red tile,
`2` blue tiles and
`1(2)/(3)` yellow tiles in each stone.