Answer :
Final answer:
By setting up a system of linear equations from the sales data provided and solving it, the cost of corsages is found to be $14 each, and boutonnieres are $22 each.
Explanation:
To solve the problem of determining the individual prices of the corsages and boutonnieres Wanda sold, we will set up a system of linear equations based on the information provided. In the first year, Wanda sold 24 corsages (C) and 36 boutonnieres (B), bringing in a total of $1,176. In the second year, she sold 33 corsages and 22 boutonnieres for a total of $1,012.
From the first year's sales, we have the equation 24C + 36B = 1176. From the second year's sales, the equation is 33C + 22B = 1012. These can be simplified (by dividing the first by 12 and the second by 11) to 2C + 3B = 98 and 3C + 2B = 92, respectively. We now have a simpler system of equations:
- 2C + 3B = 98
- 3C + 2B = 92
Solving this system will give us the individual prices of the corsages (C) and boutonnieres (B). To solve it, we can use either substitution or elimination method. Let's use elimination:
- Multiply the first equation by 3 and the second by 2: 6C + 9B = 294 and 6C + 4B = 184.
- Subtract the second equation from the first: 5B = 110.
- Solve for B: B = 22.
- Substitute B = 22 into the initial simplified equation: 2C + 3(22) = 98.
- Solve for C: C = 14.
Therefore, the corsages sell for $14 each and the boutonnieres sell for $22 each.
