Answer:
Part a) You could build 5 copies of the flower pattern
Part b) You would have 40 red trapezoids left over
Step-by-step explanation:
The complete question in the attached figure
Part a)
Let
x -----> the number of yellow hexagons
y ----> the number of red trapezoids
z ----> the number of green triangles
we know that
The flower pattern has the following ratios
![\frac{x}{y}=\frac{6}{2} ---->\frac{x}{y}=3 ----> \text {equation A}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7By%7D%3D%5Cfrac%7B6%7D%7B2%7D%20----%3E%5Cfrac%7Bx%7D%7By%7D%3D3%20----%3E%20%5Ctext%20%7Bequation%20A%7D)
![\frac{x}{z}=\frac{6}{9} -->\frac{x}{z}=\frac{2}{3} --> \text {equation B}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7Bz%7D%3D%5Cfrac%7B6%7D%7B9%7D%20--%3E%5Cfrac%7Bx%7D%7Bz%7D%3D%5Cfrac%7B2%7D%7B3%7D%20--%3E%20%5Ctext%20%7Bequation%20B%7D)
![\frac{y}{z}=\frac{2}{9} ------> \text {equation C}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7Bz%7D%3D%5Cfrac%7B2%7D%7B9%7D%20------%3E%20%5Ctext%20%7Bequation%20C%7D)
Find out how many copies of this flower pattern could you build if you had 30 yellow hexagons,50 red trapezoids, and 60 green triangles
1) For x=30
Divide 30 by 6 (remember that in one pattern there are 6 yellow hexagons)
![30/6=5\ copies](https://tex.z-dn.net/?f=30%2F6%3D5%5C%20copies)
Verify the quantity of y needed and the quantity of z needed
Find the value of y
![\frac{30}{y}=3 ---->y=30/3=10\\](https://tex.z-dn.net/?f=%5Cfrac%7B30%7D%7By%7D%3D3%20----%3Ey%3D30%2F3%3D10%5C%5C)
10 < 50 ----> is ok
Find the value of z
![\frac{30}{z}=\frac{2}{3} ---> z=30*3/2=45](https://tex.z-dn.net/?f=%5Cfrac%7B30%7D%7Bz%7D%3D%5Cfrac%7B2%7D%7B3%7D%20---%3E%20z%3D30%2A3%2F2%3D45)
45<60 --->is ok
2) For y=50
Divide 50 by 2 (remember that in one pattern there are 2 red trapezoids)
![50/2=25\ copies](https://tex.z-dn.net/?f=50%2F2%3D25%5C%20copies)
Verify the quantity of x needed and the quantity of z needed
Find the value of x
![\frac{x}{50}=3 ---->x=50*3=150](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B50%7D%3D3%20----%3Ex%3D50%2A3%3D150)
150 > 30 ----> is not ok
3) For z=60
Divide 60 by 9 (remember that in one pattern there are 9 green triangles)
60/9=6.7 copies
Round down
6 copies -----> 6(9)=54 green triangles
Verify the quantity of x needed and the quantity of y needed
Find the value of x
![\frac{x}{54}=\frac{2}{3} ---> z=54*2/3=36](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B54%7D%3D%5Cfrac%7B2%7D%7B3%7D%20---%3E%20z%3D54%2A2%2F3%3D36)
36> 30 --->is not ok
therefore
You could build 5 copies of the flower pattern
Part b)
we know that
x:y:z=6:2:9
If you build 5 copies
1) You would use 5*6=30 yellow hexagons and you would have 0 hexagons left over
2) You would use 5*2=10 red trapezoids and you would have (50-10=40) trapezoids left over
3) You would use 5*9=45 green triangles and you would have (60-45=15) triangles left over
therefore
You would have 40 red trapezoids left over