Question

A business orders 215 flowers for their employees on Valentine’s Day. Roses cost $3.00 each, carnations cost $1.00 each, and lilies 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.

Answer 1

number of Roses = 60

number of carnations = 80

number of Lilies = 75

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