The glee club needs to raise money for the spring trip to Europe, so the members are assembling holiday wreaths to sell. Before lunch, they assembled 12 regular wreaths and 18 deluxe wreaths, which used a total of 174 pinecones. After lunch, they assembled 17 regular wreaths and 13 deluxe wreaths, using a total of 159 pinecones.
How many pinecones are on a regular wreath and how many pinecones are on the deluxe wreaths?
Let's assume that there are x pinecones on a regular wreath and y pinecones on a deluxe wreath.
Before lunch, the glee club assembled 12 regular wreaths, which used a total of 12x pinecones.
They also assembled 18 deluxe wreaths, which used a total of 18y pinecones.
So, before lunch, they used a total of 12x + 18y pinecones.
After lunch, they assembled 17 regular wreaths, which used a total of 17x pinecones.
They also assembled 13 deluxe wreaths, which used a total of 13y pinecones.
So, after lunch, they used a total of 17x + 13y pinecones.
According to the information given, before lunch and after lunch, the total number of pinecones used is 174 + 159 = 333.
So we have the equation: 12x + 18y + 17x + 13y = 333.
Combining like terms, we get: 29x + 31y = 333.
Now, we need to find values of x and y that satisfy this equation. Since the number of pinecones cannot be negative, we can start by checking positive integers that are factors of 333.
When we plug in x = 3 and y = 6 into the equation, we get: 29(3) + 31(6) = 87 + 186 = 273 ≠ 333.
Similarly, when we plug in x = 6 and y = 3 into the equation, we get: 29(6) + 31(3) = 174 + 93 = 267 ≠ 333.
Trying other factors, we can see that there is no combination of x and y that satisfies the equation.
Therefore, the given information is not consistent, and there is no unique solution to this problem.