Final answer:
To solve the problem, we set up two equations representing the total number of boxes sold and the total sales. Using elimination, we find that the club sold 137 boxes of peanut wafers and 388 boxes of chocolate crisps.
Step-by-step explanation:
The student is tasked with solving a system of linear equations based on the sale of two types of cookies for a fundraiser: peanut wafers and chocolate crisps. Let's define x as the number of peanut wafer boxes sold and y as the number of chocolate crisp boxes sold. We have two equations based on the information provided:
- Equation 1 (representing the total number of boxes): x + y = 525
- Equation 2 (representing the total sales in dollars): 4x + 6y = 2876
To solve this system, we can use either substitution or elimination. For simplicity, we can multiply Equation 1 by 4 to facilitate elimination:
- 4x + 4y = 2100 (This is Equation 1 multiplied by 4)
We then subtract the new Equation 1 from Equation 2 to eliminate x:
- (4x + 6y) - (4x + 4y) = 2876 - 2100
- 2y = 776
- y = 388
With the value of y, we plug it back into Equation 1 to find x:
- x + 388 = 525
- x = 525 - 388
- x = 137
Therefore, the club sold 137 boxes of peanut wafers and 388 boxes of chocolate crisps.