How many copies of this flower pattern could you build if you had 30 yellow hexagons,50 red trapezoids, and 60 green triangles ?

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

----> ----> 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)

Verify the quantity of y needed and the quantity of z needed

Find the value of y

---->

10 < 50 ----> is ok

Find the value of z

--->

45<60 --->is ok

2) For y=50

Divide 50 by 2 (remember that in one pattern there are 2 red trapezoids)

Verify the quantity of x needed and the quantity of z needed

Find the value of x

---->

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

Verify the quantity of x needed and the quantity of y needed

Find the value of x

--->

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

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