Question

Chelsey and Brandon found 2,472 bottle caps. Brandon gave 282 bottle caps to Mason. Chelsey then had 4 times as many bottle caps as Brandon. How many bottle caps did Brandon have at first?

Answer 1

So, Brandon initially had 776 bottle caps.

Explanation:

Let's denote the initial number of bottle caps Brandon had as B and the initial number Chelsey had as C.

The total number of bottle caps they found is the sum of what Chelsey and Brandon had: B + C = 2472

After Brandon gave 282 bottle caps to Mason, he had B = 282, and Chelsey had C + 282

The problem states that Chelsey then had 4 times as many bottle caps as Brandon:

C+282=4(B−282)

Now, we have a system of two equations:

B+C=2472

C+282=4(B−282)

Let's solve this system to find the values of B and C.

From the first equation, we can express C in terms of B:

C = 2472−B

Now, substitute this expression for C into the second equation:

(2472−B) + 282 = 4(B−282)

Combine like terms:

2754−B=4B−1128

Add B to both sides:

2754 = 5B − 1128

Add 1128 to both sides:

3882 = 5B

Divide by 5:

B = 776

So, Brandon initially had 776 bottle caps.