Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. $\newline$ Sanjay is going to send some flowers to his wife. Richmond Florist charges $\$1$ per rose, plus $\$36$ for the vase. Kelly's Flowers, in contrast, charges $\$2$ per rose and $\$9$ 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? $\newline$ The cost will be $\$$ _ if the bouquet contains _ roses.

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Solve a system of equations using substitution: word problems

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

\newline

Sanjay is going to send some flowers to his wife. Richmond Florist charges

\$1

per rose, plus

\$36

for the vase. Kelly's Flowers, in contrast, charges

\$2

per rose and

\$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?

\newline

The cost will be

\$

_____ if the bouquet contains _____ roses.

Define variables: Let's define the variables: $\newline$ Let $x$ be the number of roses. $\newline$ Let $y$ be the total cost.
Equation for Richmond Florist: Write the equation for Richmond Florist: $\newline$ Richmond Florist charges $\$1$ per rose plus $\$36$ for the vase, so the equation is: $\newline$ $y = x + 36$
Equation for Kelly's Flowers: Write the equation for Kelly's Flowers: $\newline$ Kelly's Flowers charges $\$2$ per rose plus $\$9$ for the vase, so the equation is: $\newline$ $y = 2x + 9$
Set equations equal: Set the two equations equal to each other since the cost is the same: $\newline$ $x + 36 = 2x + 9$
Solve for x: Solve for x by subtracting $x$ from both sides: $\newline$ $x + 36 - x = 2x + 9 - x$ $\newline$ $36 = x + 9$
Substitute $x$ back: Subtract $9$ from both sides to solve for $x$ : $36 - 9 = x + 9 - 9$ $27 = x$
Calculate total cost: Now that we have the value of $x$ , we can substitute it back into either of the original equations to find $y$ . Let's use the first equation: $\newline$ $y = x + 36$ $\newline$ $y = 27 + 36$
Calculate total cost: Now that we have the value of $x$ , we can substitute it back into either of the original equations to find $y$ . Let's use the first equation: $\newline$ $y = x + 36$ $\newline$ $y = 27 + 36$ Calculate the total cost $y$ : $\newline$ $y = 27 + 36$ $\newline$ $y = 63$