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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineSanjay is going to send some flowers to his wife. Richmond Florist charges $1\$1 per rose, plus $36\$36 for the vase. Kelly's Flowers, in contrast, charges $2\$2 per rose and $9\$9 for the vase. If Sanjay 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 substitution, and fill in the blanks.\newlineSanjay is going to send some flowers to his wife. Richmond Florist charges $1\$1 per rose, plus $36\$36 for the vase. Kelly's Flowers, in contrast, charges $2\$2 per rose and $9\$9 for the vase. If Sanjay 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 variables: Let's define the variables:\newlineLet xx be the number of roses.\newlineLet yy be the total cost.
  2. Equation for Richmond Florist: Write the equation for Richmond Florist:\newlineRichmond Florist charges $1\$1 per rose plus $36\$36 for the vase, so the equation is:\newliney=x+36y = x + 36
  3. Equation for Kelly's Flowers: Write the equation for Kelly's Flowers:\newlineKelly's Flowers charges $2\$2 per rose plus $9\$9 for the vase, so the equation is:\newliney=2x+9y = 2x + 9
  4. Set equations equal: Set the two equations equal to each other since the cost is the same:\newlinex+36=2x+9x + 36 = 2x + 9
  5. Solve for x: Solve for x by subtracting xx from both sides:\newlinex+36−x=2x+9−xx + 36 - x = 2x + 9 - x\newline36=x+936 = x + 9
  6. Substitute xx back: Subtract 99 from both sides to solve for xx:36−9=x+9−936 - 9 = x + 9 - 927=x27 = x
  7. Calculate total cost: Now that we have the value of xx, we can substitute it back into either of the original equations to find yy. Let's use the first equation:\newliney=x+36y = x + 36\newliney=27+36y = 27 + 36
  8. Calculate total cost: Now that we have the value of xx, we can substitute it back into either of the original equations to find yy. Let's use the first equation:\newliney=x+36y = x + 36\newliney=27+36y = 27 + 36Calculate the total cost yy:\newliney=27+36y = 27 + 36\newliney=63y = 63

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