Answer:
See below
Explanation:
Rods Unit Length
Blue B x + 1
Red R x + 2
Green G 2x+1
Yellow Y 3x
We are told that:
3R + 5Y = 6G + 2Y
Let's check that claim:
3(x+2) + 5(3x) = 6(2x+1) + 2(3x)
3x + 6 + 15x = 12x + 6 + 6x
18x = 18x That is true
a. 1. Does 2R + 2Y = 4G ?
2R + 2Y = 4G
2(x+2) + 2(3x) = 4(2x+1)
2x + 4 + 6x = 8x + 4
8x + 4 = 8x + 4 YES
2. Does 3R + 3Y = 6G?
3R + 3Y = 6G
3(x+2) + 3(3x) = 6(2x+1)
3x + 6 + 9x = 12x + 6
12x + 6 = 12x + 6 YES
3. 4R + 4Y = 8G ?
4(x+2) + 4(3x) = 8(2x+1)
8x + 8 + 12x = 16x + 8
20x = 16x ? NO
b, They may be combined in various ways to produce equivalent lengths.
c> i. 3R + 1Y = 6B ?
3(x+2) + 3x = 6(x+1)
3x + 6 + 3x = 6x + 1
6 = 1 NO
ii. 6R + 2Y = 12B ?
6(x+1) + 2(3x) = 12(x+1)
6x + 6 + 6x = 12x + 12
12x + 6 = 12x + 12 NO
iii. 9R + 3Y = 18B ?
9(x + 2) + 3(3x) = 18(x+1)
9x + 18 + 9x = 18x + 18
18x + 18= 18x + 18 YES
d. They can be related to each other.