Lesson Roses and violets
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<H2>Roses and violets</H2> <H3>Problem 1</H3>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? <B>Solution</B> <pre> 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 = {{{80/4}}} = 20. Then from eq(1) 10x = 380 - 12*20 = 140 ====> x = {{{140/10}}} = 14. <U>Answer</U>. Bunch of roses costs $14. 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