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Answer:
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