There are some roses, lilies, and orchids in the vase. the number of roses is twice the number of lilies and the number of orchids is 5 more than the number of roses. if the total is 45, find the number of each type of flower

The number of roses is 16

The number of lilies is 8

The number of orchids is 21

Step-by-step explanation:

Let

x> the number of roses

y> the number of lilies

z> the number of orchids

we know that

x=2y > y=x/2 > equation A

z=x+5 ---> equation B

x+y+z=45 > equation C

substitute equation A and equation B in equation C and solve for x

x+(x/2)+(x+5)=45

(5/2)x=45-5

(5/2)x=40

x=40*2/5

x=16 roses

Find the value of y

y=x/2 > y=16/2=8 lilies

Find the value of z

z=x+5 > z=16+5=21 orchids

therefore

The number of roses is 16

The number of lilies is 8

The number of orchids is 21

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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step-by-step explanation:

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