Question

You have 350 loose batteries to put into 4 battery packs and 2 battery packs. You need to make 103 packs total. How many 4-packs and 2-packs can you make? (solve by elimination )

Answer 1

To solve the problem, we use elimination by defining x as the number of 4-packs and y as the number of 2-packs. After formulating two equations and eliminating y, we find that we can make 72 4-packs and 31 2-packs with the available batteries.

Step-by-step explanation:

The question pertains to solving a problem involving allocation and combination using the elimination method in algebra. Let's define x as the number of 4-packs and y as the number of 2-packs of batteries. We have two equations:

• 4x + 2y = 350 (total number of batteries)
• x + y = 103 (total number of packs)

By multiplying the second equation by 2, we get 2x + 2y = 206. Subtracting this from the first equation (4x + 2y = 350), we eliminate y and can solve for x:

4x + 2y - (2x + 2y) = 350 - 206
2x = 144
x = 72

Therefore, there are 72 4-packs. We can now substitute x back into the second equation to solve for y:

72 + y = 103
y = 103 - 72
y = 31

So, there are 31 2-packs. In summary, you can make 72 4-packs and 31 2-packs of batteries to fulfill the requirements with the total batteries available.