Two florist purchased flower bouquets and vases at the same store. the first florist bought 2 flower bouquets and 2 vases for a total of $12.50. the second florist bought 8 flower bouquets and 2 vases for a total of $29.00. let b represent the cost of one flower bouquet and v represent the cost of one vase. write and solve a system of equations to find the price of each type of arrangement. show all work.

We are given:  The cost of one flower bouquet =$ b.

The cost of one vase = $ v.

First florist bought: 2 flower bouquets and 2 vases.

2 *  cost of one flower bouquet + 2*cost of one vase = Total cost.

2b +2v = 12.50   equation (1).

Second florist bought: 8 flower bouquets and 2 vases.

8 *  cost of one flower bouquet + 2*cost of one vase = Total cost.

8b +2v = 29.00    equation (2).

Therefore, system of equations  we got is 2b +2v = 12.50  and 8b +2v = 29.00.

Subtracting first equation from second equation.

8b +2v = 29.00

-(2b +2v = 12.50)

6b = 16.50.

Dividing both sides by 6, we get.

b= 2.75.

Plugging b=2.75 in first equation we get

2(2.75) +2v = 12.50

5.50 +2v = 12.50

Subtracting 5.50 from both sides, we get

5.50-5.50 +2v = 12.50-5.50

2v = 7

Dividing both sides by 2, we get

v =3.50.

Therefore, cost of one flower bouquet is $2.75 and cost of one vase is $3.50.

step-by-step explanation:

ok one would be money, and the other would be refreshments or something similar. if each bag of popcorn is 5.00 and each drink is half of that that means drinks are 2.50 the proper way to do that would to look and see how much of each you can buy without exceeding a limit of 30.00

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240