A florist is creating 10 centerpieces. Roses cost $2.50 each, lilies cost $4 each, and irises cost $2 each. A customer plans on spending $300 on 10 centerpieces with each centerpiece containing 12 flowers, with twice as many roses as the number of irises and lilies combined.

a) Write a system of linear equations that represents the situation. Then write a matrix equation that corresponds to your system.

b) Find the number of flowers of each type that the florist can use to create the 10 centerpieces.

8 Roses; 1 lilie ; 3 irises

Step-by-step explanation:

Let the number of roses be 'a' , number lilies be 'b' and number of irises be 'c'

$300 for 10 centerpieces means $30 per centerpiece. therefore,

.......................(1)

also each centerpiece must contain 12 flowers, therefore,

.................................(2)

also twice as much roses as the number of irises and lilies combined

............................... (3)

a) System of equation are equations (1) , (2) & (3).

Writing a matrix equation

b) Solving the simultaneous equation,

from (3),

substituting for 'a' in equation (1) and (2),

⇒ 2.5(2b+2c)+4b+2c=30

⇒ 5b + 5c + 4b + 2c = 30

⇒ 9b + 7c = 30 ..................... (4)

⇒ 2b + 2c + b + c = 12

⇒ 3b + 3c = 12

⇒ b = 4 - c ..............................(5)

Substituting (5) in (4)

9 (4 - c) + 7c = 30

36 - 9c+7c =30

36-30 = 2c

c = 3

b = 4-3 = 1

a = 2(3+1) = 8

step-by-step explanation:

6.48/4 4 goes into 6.48 1.62 times

24

step-by-step explanation:

the graph shows 30% of students walk. 80 students were questioned, so the number that said they walk is

30% × 80 = 0.30 × 80 = 24