Lesson Roses and violets

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Roses and violets

Problem 1

Kaiden has sold 10 bunches of roses and 12 violets for a total of $380. Grayson has sold 6 bunches of roses and 8 violets for $244.
What is the cost of a bunch of roses? What is the cost of a bunch of violets?

Solution

The condition gives you this system of 2 equations in 2 unknowns 

10x + 12y = 380     (1)
 6x +  8y = 244     (2)


I will solve it by the Elimination method. For it, multiply eq(1) by 3 (both sides). Multiply eq(2) by 5. You will get

30x + 36y = 1140    (3)
30x + 40y = 1220    (4)


Next subtract eq(3) from eq(4).  The terms "30x" will cancel each other, and you will get a single equation for "y":

4y = 1220 - 1140 = 80  ====>  y =  = 20.


Then from eq(1)  10x = 380 - 12*20 = 140  ====>  x =  = 14.


Answer.  Bunch of roses costs $14.  Violet costs $20.

My other lessons in this site on solving systems of two linear equations in two unknowns (Algebra-I curriculum) are
    - Solution of the linear system of two equations in two unknowns by the Substitution method
    - Solution of the linear system of two equations in two unknowns by the Elimination method
    - Solution of the linear system of two equations in two unknowns using determinant
    - Geometric interpretation of the linear system of two equations in two unknowns
    - Useful tricks when solving systems of 2 equations in 2 unknowns by the Substitution method
    - Solving word problems using linear systems of two equations in two unknowns

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    - Using systems of equations to solve problems on tickets
    - Three methods for solving standard (typical) problems on tickets
    - Using systems of equations to solve problems on shares
    - Using systems of equations to solve problems on investment
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    - Counting calories and grams of fat in combined food
    - A theater group made appearances in two cities
    - Exchange problems solved using systems of linear equations
    - Typical word problems on systems of 2 equations in 2 unknowns
    - HOW TO algebraize and solve this problem on 2 equations in 2 unknowns
    - One unusual problem to solve using system of two equations
    - Non-standard problem with a tricky setup
    - Sometimes one equation is enough to find two unknowns in a unique way
    - Solving mentally word problems on two equations in two unknowns
    - Solving systems of non-linear equations by reducing to linear ones
    - Solving word problems for 3 unknowns by reducing to equations in 2 unknowns
    - System of equations helps to solve a problem for the Thanksgiving day
    - Using system of two equations to solve the problem for the day of April, 1

    - OVERVIEW of lessons on solving systems of two linear equations in two unknowns

Use this file/link ALGEBRA-I - YOUR ONLINE TEXTBOOK to navigate over all topics and lessons of the online textbook ALGEBRA-I.

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