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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineNolan is going to send some flowers to his wife. Clarksville Florist charges $2\$2 per rose, plus $25\$25 for the vase. Clara's Flowers, in contrast, charges $1\$1 per rose and $31\$31 for the vase. If Nolan orders the bouquet with a certain number of roses, the cost will be the same with either flower shop. What would the total cost be? How many roses would there be?\newlineThe cost will be $____\$\_\_\_\_ if the bouquet contains ____\_\_\_\_ roses.

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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineNolan is going to send some flowers to his wife. Clarksville Florist charges $2\$2 per rose, plus $25\$25 for the vase. Clara's Flowers, in contrast, charges $1\$1 per rose and $31\$31 for the vase. If Nolan orders the bouquet with a certain number of roses, the cost will be the same with either flower shop. What would the total cost be? How many roses would there be?\newlineThe cost will be $____\$\_\_\_\_ if the bouquet contains ____\_\_\_\_ roses.
  1. Define Cost Equations: Let's denote the number of roses Nolan buys as rr. According to the problem, Clarksville Florist charges $2\$2 per rose plus $25\$25 for the vase, so the total cost from Clarksville Florist can be represented as:\newlineCost at Clarksville Florist = 2r+252r + 25
  2. Set Equations Equal: Similarly, Clara's Flowers charges $1\$1 per rose plus $31\$31 for the vase, so the total cost from Clara's Flowers can be represented as:\newlineCost at Clara's Flowers = r+31r + 31
  3. Solve for rr: Since the cost will be the same with either flower shop, we can set the two expressions equal to each other to find the number of roses: 2r+25=r+312r + 25 = r + 31
  4. Isolate 'r': Now, we solve for 'r' by subtracting 'r' from both sides of the equation:\newline2r+25−r=r+31−r2r + 25 - r = r + 31 - r\newliner+25=31r + 25 = 31
  5. Calculate Total Cost: Next, we subtract 2525 from both sides to isolate 'rr':\newliner+25−25=31−25r + 25 - 25 = 31 - 25\newliner=6r = 6
  6. Calculate Total Cost: Next, we subtract 2525 from both sides to isolate 'rr':\newliner+25−25=31−25r + 25 - 25 = 31 - 25\newliner=6r = 6Now that we have the number of roses, we can calculate the total cost by plugging 'rr' back into either of the original cost equations. Let's use the Clarksville Florist equation:\newlineTotal cost = 2r+252r + 25\newlineTotal cost = 2(6)+252(6) + 25
  7. Calculate Total Cost: Next, we subtract 2525 from both sides to isolate 'rr':\newliner+25−25=31−25r + 25 - 25 = 31 - 25\newliner=6r = 6Now that we have the number of roses, we can calculate the total cost by plugging 'rr' back into either of the original cost equations. Let's use the Clarksville Florist equation:\newlineTotal cost = 2r+252r + 25\newlineTotal cost = 2(6)+252(6) + 25Perform the calculation:\newlineTotal cost = 12+2512 + 25\newlineTotal cost = 3737

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