Welcome to Star Flower Shop! This shop sells two types of flowers: lilies and roses. Each lily brings a profit of 3 yuan, while each rose brings a profit of 2 yuan. Yesterday, they sold a total of 30 flowers and earned 72 yuan in profit. Our challenge is to find out exactly how many lilies and how many roses were sold.
To solve this problem systematically, we need to define variables for our unknown quantities. Let's use x to represent the number of lilies sold and y to represent the number of roses sold. These variables will help us translate the word problem into mathematical equations that we can solve.
Now we translate our problem conditions into mathematical equations. The first condition tells us that the total number of flowers is 30, giving us the equation x plus y equals 30. The second condition states that the total profit is 72 yuan, where lilies contribute 3 yuan each and roses contribute 2 yuan each, giving us 3x plus 2y equals 72. Together, these form a system of linear equations.
Now let's solve this system using the substitution method. First, we solve the first equation for y, getting y equals 30 minus x. Next, we substitute this expression into the second equation: 3x plus 2 times the quantity 30 minus x equals 72. Expanding this gives us 3x plus 60 minus 2x equals 72, which simplifies to x equals 12. Finally, substituting back, we get y equals 18.
Now let's verify our solution. We found that x equals 12 and y equals 18. Let's check the first condition: 12 plus 18 equals 30, which matches our total flowers. For the second condition: 3 times 12 plus 2 times 18 equals 36 plus 36, which equals 72 yuan, matching our total profit. Both conditions are satisfied! Therefore, the flower shop sold 12 lilies and 18 roses yesterday.