Emily makes 75 pins to sell at the school craft fair She has two designs, a star and a bumblebee. She makes 2 star pins for every 3 bumblebee pins. How many pins of each rype does Emily moke? Show your work.

To find out how many star and bumblebee pins Emily makes, let's denote the number of star pins as \( S \) and the number of bumblebee pins as \( B \). According to the problem, the ratio of star pins to bumblebee pins is 2:3. We can set this up as: \[ S = \frac{2}{3}B \] Additionally, we know that the total number of pins she makes is 75: \[ S + B = 75 \] Now we can substitute the expression for \( S \) into the total equation: \[ \frac{2}{3}B + B = 75 \] Combining like terms: \[ \frac{2}{3}B + \frac{3}{3}B = 75 \] \[ \frac{5}{3}B = 75 \] Now, multiply each side by 3 to eliminate the fraction: \[ 5B = 225 \] Next, divide each side by 5: \[ B = 45 \] Now that we have the number of bumblebee pins, we can find the number of star pins: \[ S = \frac{2}{3} \times 45 = 30 \] Thus, Emily makes 30 star pins and 45 bumblebee pins.