Answer:
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.