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)
<u><em>Verify the quantity of y needed and the quantity of z needed</em></u>
<em>Find the value of y</em>
---->
10 < 50 ----> is ok
<em>Find the value of z</em>
--->
45<60 --->is ok
2) For y=50
Divide 50 by 2 (remember that in one pattern there are 2 red trapezoids)
<u><em>Verify the quantity of x needed and the quantity of z needed</em></u>
<em>Find the value of x</em>
---->
150 > 30 ----> is not ok
3) For z=60
Divide 60 by 9 (remember that in one pattern there are 9 green triangles)
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>
--->
36> 30 --->is not ok
therefore
You could build 5 copies of the flower pattern
Part b) we know that
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