Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. $\newline$ Kirk is going to send some flowers to his wife. Lakeside Florist charges $\$1$ per rose, plus $\$36$ for the vase. Colette's Flowers, in contrast, charges $\$2$ per rose and $\$10$ for the vase. If Kirk 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? $\newline$ If the bouquet contains $\_\_$ roses, it will cost $\$\_\_$ .

View step-by-step help

Home

Math Problems

Algebra 1

Solve a system of equations using any method: word problems

Full solution

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

\newline

Kirk is going to send some flowers to his wife. Lakeside Florist charges

\$1

per rose, plus

\$36

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

\$2

per rose and

\$10

for the vase. If Kirk 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?

\newline

If the bouquet contains

\_\_

roses, it will cost

\$\_\_

Set up equations: Set up the equations based on the given information. $\newline$ Lakeside Florist: Cost = $\$1$ per rose + $\$36$ for the vase. $\newline$ Colette's Flowers: Cost = $\$2$ per rose + $\$10$ for the vase. $\newline$ Since the cost is the same for both, we can write the equations as: $\newline$ $1 \times \text{number of roses} + 36 = 2 \times \text{number of roses} + 10$ $\newline$ Let's denote the number of roses as ' $r$ '.
Write system: Write the system of equations. $\newline$ Lakeside Florist: $1r + 36$ $\newline$ Colette's Flowers: $2r + 10$ $\newline$ Since the costs are equal, we have: $\newline$ $1r + 36 = 2r + 10$
Solve equations: Solve the system of equations. $\newline$ Subtract $1r$ from both sides to get the roses on one side: $\newline$ $1r + 36 - 1r = 2r + 10 - 1r$ $\newline$ $36 = r + 10$ $\newline$ Now, subtract $10$ from both sides to solve for $r$ : $\newline$ $36 - 10 = r + 10 - 10$ $\newline$ $26 = r$
Find total cost: Find the total cost. $\newline$ Now that we know the number of roses is $26$ , we can plug this into either florist's cost equation to find the total cost. Let's use Lakeside Florist's equation: $\newline$ Cost $= 1 \times 26 + 36$ $\newline$ Cost $= 26 + 36$ $\newline$ Cost $= \$(62)$
Verify solution: Verify the solution with Colette's Flowers' cost equation. $\newline$ Cost = $2 \times 26 + 10$ $\newline$ Cost = $52 + 10$ $\newline$ Cost = $\$62$ $\newline$ Since the cost is the same for both florists, our solution is correct.