Ellen is laying out a design for the tiles on part of a kitchen back splash. She will
use 2 brown tiles for every 3 gold tiles to have a total of 15 tiles in the design.
How many of each color tile will be in the design
6+9 = 15
To determine the number of each color tile in the design, we can set up a proportion based on the given information.
Let's assume the number of brown tiles is represented by "x" and the number of gold tiles is represented by "y".
According to the given information, Ellen will use 2 brown tiles for every 3 gold tiles. This can be expressed as the following ratio:
2/3 = x/y
We also know that the total number of tiles in the design is 15. Therefore, we have the equation:
x + y = 15
To solve this system of equations, we can use the method of substitution or elimination. In this case, let's solve by substitution.
From the first equation, we can express "x" in terms of "y":
2/3 = x/y
2 = (2/3)y
2 = 2y/3
2 * 3 = 2y
6 = 2y
y = 6/2
y = 3
Now, substitute the value of "y" into the second equation:
x + y = 15
x + 3 = 15
x = 15 - 3
x = 12
Therefore, there will be 12 brown tiles and 3 gold tiles in the design.
To solve this problem, we can set up a proportion based on the given information.
Let's assume "x" represents the number of brown tiles, and "y" represents the number of gold tiles.
According to the problem, Ellen will use 2 brown tiles for every 3 gold tiles. Therefore, the ratio of brown tiles to gold tiles can be expressed as 2/3.
We can set up the proportion as follows:
x/y = 2/3
Now, we know that the total number of tiles in the design is 15. So we can create an equation based on this information:
x + y = 15
To solve this system of equations, we can use substitution or elimination method.
Let's solve it using substitution method:
From the first equation, we can isolate x:
x = (2/3)y
Now substitute this value of x in the second equation:
(2/3)y + y = 15
(2y + 3y)/3 = 15
5y/3 = 15
Multiply both sides of the equation by 3 to get rid of the fraction:
5y = 45
Divide both sides of the equation by 5 to isolate y:
y = 9
Now substitute this value of y back into one of the original equations to find x:
x = (2/3)(9)
x = 6
Therefore, there will be 6 brown tiles and 9 gold tiles in the design.