A business orders 330 flowers for their employees on Valentine's Day. Roses cost
$4.50 each, carnations cost $3.00 each, and lilies cost $2.50 each. There are 20
more lilies than roses. The total of the order came to $1,080.00. How many of each
type of flower were ordered? Write a system of equations that represents the
scenario.

Question

03-10-2020
Mathematics

contestada

A business orders 330 flowers for their employees on Valentine's Day. Roses cost
$4.50 each, carnations cost $3.00 each, and lilies cost $2.50 each. There are 20
more lilies than roses. The total of the order came to $1,080.00. How many of each
type of flower were ordered? Write a system of equations that represents the
scenario.

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adioabiola adioabiola · Answer 1 · 2020-10-10T02:23:44+02:00

Answer:

Roses = x = 100

Carnations = y = 110

Lilies = z = 120

Step-by-step explanation:

Roses = $4.50

Carnations = $3.00

lilies = $2.50

Total flowers ordered = 330

Total cost = $1,080

Let

Roses = x

Carnations = y

Lilies = z

x + y + z = 330

4.50x + 3y + 2.50z = 1080

There are 20

more lilies than roses

z = x + 20

Substitute z = x + 20 into the equations

x + y + (x + 20) = 330

4.50x + 3y + 2.50(x + 20) = 1080

x + y + x + 20 = 330

4.50x + 3y + 2.50x + 50 = 1080

2x + y = 330 - 20

7x + 3y = 1080 - 50

2x + y = 310 (1)

7x + 3y = 1030 (2)

Multiply (1) by 3

6x + 3y = 930 (3)

7x + 3y = 1030 (2)

Subtract (3) from (2)

7x - 6x = 1030 - 930

x = 100

Substitute x = 100 into (1)

2x + y = 310

2(100)+ y = 310

200 + y = 310

y = 310 - 200

= 110

y = 110

Substitute the value of x and y into

x + y + z = 330

100 + 110 + z = 330

210 + z = 330

z = 330 - 210

= 120

z = 120

Roses = x = 100

Carnations = y = 110

Lilies = z = 120