A business orders 215 flowers for their employees on Valentine’s Day. Roses cost $3.00 each, carnations cost $1.00 each, and lil ies cost $2.00 each. There are 15 more lilies than roses. The total of the order came to $410.00. How many of each type of flower were ordered? How many of each type of flower were ordered?
Write the system of equations that represents this scenario.
1 answer:
Answer:
number of Roses = 60
number of carnations = 80
number of Lilies = 75
Step-by-step explanation:
Roses = $3.00
carnations = $1.00
Lilies = $2.00
Total order = 215
Let
x = number of Roses
y = number of carnations
z = number of Lilies
There are 15 more lilies than roses.
z = x + 15
The total of the order came to $410.00.
x + y + z = 215
3x + y + 2z = 410
substitute z = x + 15
x + y + x + 15 = 215
3x + y + 2(x+15) = 410
2x + y + 15= 215
3x + y + 2x + 30 = 410
2x + y = 215 - 15
5x + y = 410 - 30
2x + y = 200 (1)
5x + y = 380 (2)
Subtract (1) from (2)
5x - 2x = 380 - 200
3x = 180
Divide both sides by 3
x = 180/3
= 60
x = 60
Recall
z = x + 15
z = 60 + 15
= 75
z = 75
Substitute the value of x into (1)
2x + y = 200
2(60) + y = 200
120 + y = 200
y = 200 - 120
= 80
y = 80
Therefore,
x = number of Roses = 60
y = number of carnations = 80
z = number of Lilies = 75
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