Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Eddie is going to send some flowers to his wife. Greenpoint Florist charges $1 per rose, plus $15 for the vase. Dakota's Flowers, in contrast, charges $2 per rose and $10 for the vase. If Eddie 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.  Eddie is going to send some flowers to his wife. Greenpoint Florist charges $1 per rose, plus $15 for the vase. Dakota's Flowers, in contrast, charges $2 per rose and $10 for the vase. If Eddie 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 $_____.

Bytelearn · Accepted Answer

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.Equation for Greenpoint Florist: We can write the equation for Greenpoint Florist as follows: y = $1 * x + $15 (cost per rose * number of roses + cost of vase) So, the equation is y = x + 15.Equation for Dakota's Flowers: We can write the equation for Dakota's Flowers as follows: y = $2 * x + $10 (cost per rose * number of roses + cost of vase) So, the equation is y = 2x + 10.System of Equations: Now we have a system of equations: 1. y = x + 15 (Greenpoint Florist) 2. y = 2x + 10 (Dakota's Flowers) We will use substitution to solve for x by setting the two equations equal to each other since the cost y is the same.Set Equations Equal: Setting the two equations equal to each other: x + 15 = 2x + 10 Now, we solve for x.Solve for x: Subtract x from both sides of the equation: x + 15 - x = 2x + 10 - x This simplifies to: 15 = x + 10Substitute x: Subtract 10 from both sides of the equation: 15 - 10 = x + 10 - 10 This simplifies to: 5 = xFind Total Cost: Now that we have the value of x, we can find the total cost y by substituting x into either of the original equations. Let's use the first equation from Greenpoint Florist: y = x + 15 y = 5 + 15 y = 20Final Result: We have found that the bouquet contains 5 roses and it will cost $20 at both flower shops.

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