Question

The tile backslash will be a mixture of colors of five-inch square tiles. One quarter of the tiles will be "Indian Red" one sixth will be "Tuscan Blue", one fifth will be "Eucalyptus", and the rest will be the color "Sand". What fraction of the tiles will be the color of "Sand"

Answer 1

The fraction of tiles that will be the color of "sand" is 23/60

Explanation:

we know that

The sum of the fractions of the tiles must be equal to 1

Let

x ----> the fraction of tiles that will be the color of "sand"

we have that

`(1)/(4)+(1)/(6)+(1)/(5)+x=1`

solve for x

Find the Least Common Multiple of denominators

`LCM=(2^2)((3)(5)=60`

Multiply both sides by 60

`(60)/(4)+(60)/(6)+(60)/(5)+60x=60`

simplify

`15+10+12+60x=60`

`60x=60-37\\60x=23\\x=(23)/(60)`

therefore

The fraction of tiles that will be the color of "sand" is 23/60