Melanie gave her mother a bouquet of 24 flowers. The bouquet was made up of roses, carnations, and daisies. There were twice as many daisies as roses. There were three times as many carnations as roses. How many of each kind of flower was in the bouquet?

Roses = x = 4

Carnations = y = 12

Daisies = z = 8

Step-by-step explanation:

The bouquet was made up of roses, carnations, and daisies.

Let us represent:

Roses = x

Carnations = y

Daisies = z

Melanie gave her mother a bouquet of 24 flowers.

Hence,

x + y + z = 24 Equation 1

There were twice as many daisies as roses.

z = 2x

There were three times as many carnations as roses.

y = 3x

Therefore, we substitute 2x and 3x for z and y respectively in Equation 1

x + y + z = 24 Equation 1

x + 3x + 2x = 24

6x = 24

x = 24/6

x = 4 roses

Solving for y

y = 3x

y = 3 × 4

y = 12 Carnations

Solving for z

z = 2x

z = 2 × 4

z = 8 Daisies

How many of each kind of flower was in the bouquet?

Therefore,

Roses = x = 4

Carnations = y = 12

Daisies = z = 8

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west