Answer:
The fraction of tiles that will be the color of "sand" is 23/60
Step-by-step 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
[tex]\frac{1}{4}+\frac{1}{6}+\frac{1}{5}+x=1[/tex]
solve for x
Find the Least Common Multiple of denominators
[tex]LCM=(2^2)((3)(5)=60[/tex]
Multiply both sides by 60
[tex]\frac{60}{4}+\frac{60}{6}+\frac{60}{5}+60x=60[/tex]
simplify
[tex]15+10+12+60x=60[/tex]
[tex]60x=60-37\\60x=23\\x=\frac{23}{60}[/tex]
therefore
The fraction of tiles that will be the color of "sand" is 23/60
