Question

brianne is buying flowers for the centerpiece in her clients wedding reception. her client said she wants only roses and carnations in the centerpieces. she purchases r bouquets of roses and c bouquets of carnations. roses cost $25.80 per bouq 6 n carnations cost 18.55 per bouquet . brianne spent a total of $5096 on flowers for her client and bought 220 bouquet altogether. A. write a system of equations to represent the constraints in this situation.B. how many bouquets of Carnations did brianne putchase.C. explain or show your reasoning for the number of carnations stated in your answer to the previous question. thats the problems were working on

Answer 1

Part A.

r + c = 220

25.80r + 18.55c = 5096

Part B.

c = 80

Part C.

Solve the first equation for r and replace it on the second equation. Finally, solve for c.

Step-by-step explanation:

r is the number of bouquets of roses and c is the number of bouquets of carnations.

We know that she bought 220 bouquets altogether, so we can write the following equation:

r + c = 220

Additionally, each bouquet of roses costs $25.80 and each bouquet of carnations costs $18.55. If the total spent was $5096, we can write the following equation:

25.80r + 18.55c = 5096

Because 25.80 times r is the total cost of the roses and 18.55 times c is the total cost of the carnations.

Part A.

Now, we have the following system of equations

r + c = 220

25.80r + 18.55c = 5096

Part C.

To find the number of carnations, we need to solve the first equation for r, so

r + c = 220

r + c - c = 220 - c

r = 220 - c

Then, we need to replace r = 220 - c on the second equation:

25.80r + 18.55c = 5096

25.80(220 - c) + 18.55c = 5096

Solving for c, we get:

25.80(220) - 25.80c + 18.55c = 5096

5676 - 7.25c = 5096

5676 - 7.25c + 7.25c = 5096 + 7.25c

5676 = 5096 + 7.25c

5676 - 5096 = 5096 + 7.25c - 5096

580 = 7.25c

580/7.25 = 7.25c/7.25

80 = c

Part B.

Therefore, the number of bouquets of carnations is 80.