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.

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