There are 43 tiles in a bag. The colors are red, blue, green and yellow. Find the
number of each color tile given the following ratios:
red : blue = 2 : 3 blue : green = 2 : 1 green : yellow = 2 : 5
what is the number of tiles of each color??
Question
Answer:
43/13, 129/26, 129/13, 645/26
Step-by-step explanation:
Let w represent the number of red tiles, x represent the number of blue tiles, y represent the number of green tiles and z represent the number of yellow tiles. Hence:
w + x + y + z = 43 (1)
x = 3/5(w + x)
2x/5 = 3w/5
x = 3/2(w)
x = 5w/2 – w = 3w/2 (2)
y = 2/3(x + y)
y/3 = 2x/3
y = 2x = 2(3w/2) = 3w (3)
z = 5/7(y + z)
2/7(z) = 5y/7
z = 5y/2 = 5(3w)/2 = 15w/2 (4)
substitute x = 3w/2, y = 3w and z = 15w/2 in equation 1:
w + 3w/2 + 3w + 15w/2 = 43
13w = 43
w = 43/13
x = 129/26
y = 3w = 129/13
z = 645/26