Respuesta :
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
