Question

Write a system of equations to describe the situation below, solve usingsubstitution, and fill in the blanks.Mrs. Vega is researching what it would cost to order flower arrangements for afancy party. She wants one large centerpiece for the head table, and smallerarrangements for the smaller tables. Sparrowtown Florist charges $13 for eachsmaller arrangement, plus $29 for the large centerpiece. Michelle's Flowers, incontrast, charges $51 for the large centerpiece and $12 per arrangement forthe rest. If Mrs. Vega orders a certain number of small arrangements, the costwill be the same at either flower shop. How many small arrangements wouldthat be? What would the total cost be?small arrangements, it will cost $atIf Mrs. Vega orderseither shop.

Answer 1

Given:

The cost of a smaller arrangement by Sparrowtown Florist, s=$13.

The cost of a large centerpiece by Sparrowtown Florist, S=$29.

The cost of a smaller arrangement by Michelle's Flowers, m=$12

The cost of a large centerpiece by Michelle's Flowers, M=$51.

Let x be the number of smaller arrangements ordered by Vega from Sparrowtown Florist and y be the number of smaller arrangements ordered by Vega from Michelle's Flowers.

Given, the cost of smaller arrangements ordered by Vega will be the same at either flower shop.

The cost of smaller arrangement ordered from Sparrowtown Florist is,

`T=sx`

The cost of smaller arrangement ordered from Michelle's Flowers is,

`T=my`

Hence,

`\begin{gathered} sx=my \\ 13x=12y\ldots\ldots(1) \\ (x)/(y)=(12)/(13) \end{gathered}`

Using the above ratio , we can write, x=13n and y=12n where n is a constant. Let n=1.

If we put x=12 and y=13 in equation (1),

`\begin{gathered} 13*12=12*13 \\ 156=156 \end{gathered}`

Hence, the number of smaller arrangements is,

`\begin{gathered} t=x+y \\ =12+13 \\ =25 \end{gathered}`

Now, the total cost of smaller arrangements per shop is,

`\begin{gathered} T=sx \\ =13*12 \\ =156 \end{gathered}`

Hence, if Vega orders 25 smaller arrangements, it will cost $156 at either shop