Carrie has a home-based business making corsages and boutonnieres for school dances. Last year, she sold 12 corsages and 31 boutonnieres, which brought in a total of $972. This year, she sold 33 corsages and 30 boutonnieres, for a total of $1,347. How much does each item sell for?

The question is missing the figure. So, the figure is attached below.

SSS

SAS

ASA

Step-by-step explanation:

Given:

Quadrilateral STRU is a parallelogram.

A parallelogram is a quadrilateral in which the opposite sides are parallel an equal to each other.

Case 1:

So, for Δ RTS and Δ TRU

RS ≅ TU     [ Definition of a parallelogram]

ST ≅ RU     [ Definition of a parallelogram]

RT ≅ RT      [Common side; Reflexive property]

Therefore, the triangles are congruent by SSS postulate.

Case 2:

∠4 ≅ ∠8     [ Alternate interior angles are equal]

RT ≅ RT      [Common side; Reflexive property]

∠3 ≅ ∠7      [ Alternate interior angles are equal]

Therefore, the triangles are congruent by ASA postulate.

Case 3:

RS ≅ TU     [ Definition of a parallelogram]

∠4 ≅ ∠8     [ Alternate interior angles are equal]

RT ≅ RT      [Common side; Reflexive property]

Therefore, the triangles are congruent by SAS postulate.