Two sunflowers and a rose cost \( \$ 5.50 \). Three sunflowers and two roses cost \( \$ 9.50 \).

To untangle the cost of a sunflower and a rose, let's set up some equations! Let \( S \) represent the cost of a sunflower and \( R \) represent the cost of a rose. From the first piece of information, we get: 1) \( 2S + R = 5.50 \) From the second, we can derive: 2) \( 3S + 2R = 9.50 \) Now, solving this system of equations will help us find the individual costs of the sunflowers and the rose! If we multiply the first equation by 2, we can align it with the second equation for easier subtraction: \( 4S + 2R = 11.00 \) Now, subtract the second equation from this new equation: \( (4S + 2R) - (3S + 2R) = 11.00 - 9.50 \) This simplifies to: \( S = 1.50 \) Now, substituting \( S \) back into one of our original equations to find \( R \): \( 2(1.50) + R = 5.50 \) \( 3.00 + R = 5.50 \) Thus, \( R = 2.50 \). So, a sunflower costs \( \$1.50 \) and a rose costs \( \$2.50 \). Now you can ace any flower shop experience!