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 get2(2.75) +2v = 12.50 5.50 +2v = 12.50Subtracting 5.50 from both sides, we get 5.50-5.50 +2v = 12.50-5.502v = 7Dividing 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.