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

Part a) You could build 5 copies of the flower pattern

Part b) You would have 40 red trapezoids left over

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

`(x)/(y)=(6)/(2)` ---->
`(x)/(y)=3` ----> equation A

`(x)/(z)=(6)/(9)` -->
`(x)/(z)=(2)/(3)` --> equation B

`(y)/(z)=(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

`(30)/(y)=3` ---->
`y=30/3=10`

10 < 50 ----> is ok

Find the value of z

`(30)/(z)=(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

`(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

`(x)/(54)=(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