Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Franco is going to send some flowers to his wife. Westford Florist charges $1 per rose, plus $20 for the vase. Nate's Flowers, in contrast, charges $3 per rose and $18 for the vase. If Franco orders the bouquet with a certain number of roses, the cost will be the same with either flower shop. How many roses would there be? What would the total cost be? If the bouquet contains _____ roses, it will cost $_____.

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.  Franco is going to send some flowers to his wife. Westford Florist charges $1 per rose, plus $20 for the vase. Nate's Flowers, in contrast, charges $3 per rose and $18 for the vase. If Franco orders the bouquet with a certain number of roses, the cost will be the same with either flower shop. How many roses would there be? What would the total cost be?   If the bouquet contains _____ roses, it will cost $_____.

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Define Variables: Let's define the variables: Let x be the number of roses in the bouquet. Let y be the total cost of the bouquet.Write Westford Florist Equation: We can write the equation for Westford Florist as follows: y = $1 * x + $20 (Cost per rose * Number of roses + Cost of vase) So, the equation is y = x + 20.Write Nate's Flowers Equation: We can write the equation for Nate's Flowers as follows: y = $3 * x + $18 (Cost per rose * Number of roses + Cost of vase) So, the equation is y = 3x + 18.Set Equations Equal: Now we have two equations: 1) y = x + 20 (Westford Florist) 2) y = 3x + 18 (Nate's Flowers) Since the total cost y is the same for both, we can set the equations equal to each other to solve for x. x + 20 = 3x + 18Subtract x: Subtract x from both sides to start solving for x: x + 20 - x = 3x + 18 - x 20 = 2x + 18Subtract 18: Subtract 18 from both sides to isolate the term with x: 20 - 18 = 2x + 18 - 18 2 = 2xDivide by 2: Divide both sides by 2 to solve for x: 2 / 2 = 2x / 2 1 = xFind Total Cost: Now that we have the number of roses x, we can find the total cost y using either of the original equations. Let's use the equation from Westford Florist: y = x + 20 y = 1 + 20 y = $21Final Result: We have found that the bouquet contains 1 rose and it will cost $21 at both Westford Florist and Nate's Flowers.

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