Answer :
Answer: 1/3
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Explanation:
1/5 of the tiles are indian red
3/10 of the tiles are Tuscan blue
1/6 of the tiles are eucalyptus
x of the tiles are sand, where x is some fraction
The four fractions listed above add to 1. The "1" refers to a whole back splash, in which you can think of "1" as "100%"
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We have the fractions 1/5, 3/10 and 1/6
To combine these fractions, we need a common denominator. In this case, the lowest common denominator (LCD) is 30 as this is the LCM of the denominators 5, 10, and 6.
Let's get each fraction to have a denominator of 30
1/5 = (6/6)*(1/5) = 6/30
3/10 = (3/3)*(3/10) = 9/30
1/6 = (5/5)*(1/6) = 5/30
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So effectively we have these fractions: 6/30, 9/30, and 5/30
They add to the unknown fraction x to get 1
Let's solve for x.
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(1/5) + (3/10) + (1/6) + x = 1
(6/30) + (9/30) + (5/30) + x = 1
(6/30 + 9/30 + 5/30) + x = 1
(6 + 9 + 5)/30 + x = 1
20/30 + x = 1
2/3 + x = 1
x + 2/3 = 1
x+2/3-2/3=1-2/3 ... subtract 2/3 from both sides
x = 1 - 2/3
x = 3/3 - 2/3
x = (3 - 2)/3
x = 1/3
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1/3 of the tiles are the color of sand