Question

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

Answer 1

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

$\frac{x}{y}=\frac{6}{2}$ ---->$\frac{x}{y}=3$ ----> equation A

$\frac{x}{z}=\frac{6}{9}$ -->$\frac{x}{z}=\frac{2}{3}$ --> equation B

$\frac{y}{z}=\frac{2}{9}$ ------> 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)

$30/6=5\ copies$

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

Find the value of y

$\frac{30}{y}=3$ ---->$y=30/3=10$

10 < 50 ----> is ok

Find the value of z

$\frac{30}{z}=\frac{2}{3}$ ---> $z=30*3/2=45$

45<60 --->is ok

2) For y=50

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

$50/2=25\ copies$

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

Find the value of x

$\frac{x}{50}=3$ ---->$x=50*3=150$

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

$\frac{x}{54}=\frac{2}{3}$ ---> $z=54*2/3=36$

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