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
[tex]\frac{x}{y}=\frac{6}{2}[/tex] ---->[tex]\frac{x}{y}=3[/tex] ----> equation A
[tex]\frac{x}{z}=\frac{6}{9}[/tex] -->[tex]\frac{x}{z}=\frac{2}{3}[/tex] --> equation B
[tex]\frac{y}{z}=\frac{2}{9}[/tex] ------> 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)
[tex]30/6=5\ copies[/tex]
Verify the quantity of y needed and the quantity of z needed
Find the value of y
[tex]\frac{30}{y}=3[/tex] ---->[tex]y=30/3=10[/tex]
10 < 50 ----> is ok
Find the value of z
[tex]\frac{30}{z}=\frac{2}{3}[/tex] ---> [tex]z=30*3/2=45[/tex]
45<60 --->is ok
2) For y=50
Divide 50 by 2 (remember that in one pattern there are 2 red trapezoids)
[tex]50/2=25\ copies[/tex]
Verify the quantity of x needed and the quantity of z needed
Find the value of x
[tex]\frac{x}{50}=3[/tex] ---->[tex]x=50*3=150[/tex]
150 > 30 ----> is not ok
3) For z=60
Divide 60 by 9 (remember that in one pattern there are 9 green triangles)
[tex]60/9=6.7\ copies[/tex]
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
[tex]\frac{x}{54}=\frac{2}{3}[/tex] ---> [tex]z=54*2/3=36[/tex]
36> 30 --->is not ok
therefore
You could build 5 copies of the flower pattern
Part b) we know that
[tex]x:y:z=6:2:9[/tex]
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
