Answer :
To determine the prices of corsages and boutonnieres sold by Barbara, we set up a system of equations with two unknowns representing the prices and solve it.
To solve this problem, we need to set up a system of equations. Let's let x be the price of one corsage and let y be the price of one boutonniere. From the information provided, we can write our equations based on the number of corsages and boutonnieres sold and the total revenue in each year.
Last year's equation: 28x + 26y = 1426
This year's equation: 40x + 35y = 1975
Now, we will solve this system of equations using a method such as substitution or elimination to find the values of x and y.