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:
<u><em>The complete question in the attached figure</em></u>
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
---->
----> equation A
-->
--> equation B
------> equation C
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)
<u><em>Verify the quantity of y needed and the quantity of z needed</em></u>
<em>Find the value of y</em>
---->![y=30/3=10](https://tex.z-dn.net/?f=y%3D30%2F3%3D10)
10 < 50 ----> is ok
<em>Find the value of z</em>
---> ![z=30*3/2=45](https://tex.z-dn.net/?f=z%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)
<u><em>Verify the quantity of x needed and the quantity of z needed</em></u>
<em>Find the value of x</em>
---->![x=50*3=150](https://tex.z-dn.net/?f=x%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](https://tex.z-dn.net/?f=60%2F9%3D6.7%5C%20copies)
Round down
6 copies -----> 6(9)=54 green triangles
<u><em>Verify the quantity of x needed and the quantity of y needed</em></u>
<em>Find the value of x</em>
---> ![z=54*2/3=36](https://tex.z-dn.net/?f=z%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](https://tex.z-dn.net/?f=x%3Ay%3Az%3D6%3A2%3A9)
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