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 14 deluxe wreaths, which used a total of 160 pinecones. After lunch, they assembled 15 regular wreaths and 15 deluxe wreaths, using a total of 180 pinecones. How many pinecones are they putting on a regular wreath and how many pinecones on a deluxe wreath?
Let's represent the number of pinecones on a regular wreath as "r" and the number of pinecones on a deluxe wreath as "d".
Before lunch, they assembled 12 regular wreaths, so they used 12r pinecones for the regular wreaths.
Before lunch, they assembled 14 deluxe wreaths, so they used 14d pinecones for the deluxe wreaths.
Thus, before lunch, they used a total of 12r + 14d pinecones.
After lunch, they assembled 15 regular wreaths, so they used 15r pinecones for the regular wreaths.
After lunch, they assembled 15 deluxe wreaths, so they used 15d pinecones for the deluxe wreaths.
Thus, after lunch, they used a total of 15r + 15d pinecones.
We know that before lunch, they used a total of 160 pinecones, so we can equate the two expressions for pinecones used:
12r + 14d = 160.
We also know that after lunch, they used a total of 180 pinecones, so we can equate the two expressions for pinecones used:
15r + 15d = 180.
To solve this system of equations, we can simplify each equation:
6r + 7d = 80,
r + d = 12.
We can solve the second equation for r:
r = 12 - d.
Substituting this into the first equation, we get:
6(12 - d) + 7d = 80,
72 - 6d + 7d = 80,
d = 8.
Substituting this value of d back into the second equation, we get:
r + 8 = 12,
r = 4.
Therefore, there are 4 pinecones on a regular wreath and 8 pinecones on a deluxe wreath.