Jennifer bought some tulips, lilies, and roses to make bouquets. She bought the same number of tulips as lilies. She bought three more roses than tulips and lilies combined. She paid 18 cents for each tulip. The lilies were 27 cents per flower, and the roses cost 55 cents each. How many of each kind of flower did Jennifer buy if she paid $17.15 in all?

10 tulips, 10 lilies and 23 roses.

Step-by-step explanation:

Let's define the variables:

T = number of tulips that Jennifer bought

L = number of lilies that Jennifer bought

R = number of roses that Jennifer bought

Each tulip costs $0.18

Each lily costs $0.27

Each rose costs $0.55

We know that:

"She bought the same number of tulips as lilies."

T = L

" She bought three more roses than tulips and lilies combined."

R = T + L + 3

"she paid $17.15 in all"

T*$0.18 + L*$0.27 + R*$0.55 = $17.15

Then we have a system of 3 equations:

T = L

R = T + L + 3

T*$0.18 + L*$0.27 + R*$0.55 = $17.15

The first step to solve this is to replace the first equation into the other two, and get:

R = 2*L + 3

L*$0.18 + L*$0.27 + R*$0.55 = $17.15

Now we can replace the first equation into the second:

L*$0.18 + L*$0.27 + (2*L + 3)*$0.55 = $17.15

Now we can solve this for L.

L*($0.18 + $0.27 + 2*$0.55) + 3*$0.55 = $17.15

L*$1.55 + $1.66 = $17.15

L*$1.55 = $17.15 - $1.66 = $15.50

L = $15.50/$1.55 = 10

Then Jennifer bought 10 lilies.

And by the other two equations:

T = L = 10

She bought 10 tulips.

R = L + T + 3 = 10 + 10 + 3 = 23

She bought 23 roses

c is the final answer! : )

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)