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

Reba has a home-based business making corsages and boutonnieres for school dances. Last year, she sold 35 corsages and 29 boutonnieres, which brought in a total of $1,408. This year, she sold 24 corsages and 15 boutonnieres, for a total of $858. How much does each item sell for?

A corsage sells for $________, and a boutonniere sells for $________.

Answer :

The amount a corsage and a boutonniere sells for this year is taken as

the same as the amount they where sold last year.

The system of equations is presented as follows;

  • 35·x + 29·y = 1,408
  • 24·x + 15·y = 858

  • A corsage sells for $22, and a boutonniere sells for $22

Methods uses to write a system of equations

Last year, she sold 35 corsages and 29 boutonnieres = $1,408

This year, she sold 24 corsages and 15 boutonnieres = $858

Required:

How much does each item sell for

Solution:

Let x represent the price of each corsages, and let y represent the price

of each boutonnieres sold, we have, the following system of equations;

  • 35·x + 29·y = 1,408...(1)
  • 24·x + 15·y = 858...(2)

Making y the subject of equation (1), gives;

  • [tex]y = \mathbf{\dfrac{1,408}{29} - \dfrac{35}{29} \cdot x}[/tex]

Therefore;

[tex]24 \cdot x + 15 \times \left(\dfrac{1,408}{29} - \dfrac{35}{29} \cdot x \right) = \mathbf{\dfrac{171\cdot x + 21120}{29}} = 858[/tex]

171·x + 21120 = 858 × 29 = 24,882

171·x = 24,882 - 21,120 = 3,762

  • [tex]x = \dfrac{3,762}{171} = \mathbf{22}[/tex]

Therefore;

  • Each corsage sells for, x = $22

[tex]y = \mathbf{\dfrac{1,408}{29} - \dfrac{35}{29} \times 22} = 22[/tex]

  • Each boutonniere sells for, y = $22

Learn more about writing a system of equations here:

https://brainly.com/question/10722225

Final answer:

The system of equations describing the given situation is 35C + 29B = $1408 and 24C + 15B = $858. After solving this system, we find that a corsage costs $25 and a boutonniere costs $19.

Explanation:

Solution:

Let's denote the price of a corsage as C and the price of a boutonniere as B. We can write two equations based on the given information:

1) 35C + 29B = $1408
2) 24C + 15B = $858

Next, we need to solve this system of equations. To do this, we can use the substitution or elimination method. I will choose the substitution method for its simplicity.

Let’s manipulate the second equation and solve for C: C = (858 - 15B) / 24

Now replace C in the first equation with (858 - 15B) / 24 and solve for B: 35*(858 - 15B) / 24 + 29B = 1408 After solving this equation we find that B = $19.

Substituting B into the second equation we find that C = $25.

So, a boutonniere sells for $19 and a corsage sells for $25.

Learn more about System of Equations here:

https://brainly.com/question/35467992

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