Two boxes of apples contain a total of 24 apples. If you have the number of apples in the first box and add 4 apples to the second box, the total
changes to 20 apples. How many apples are in each box initially?
OA. 12 and 12
OB. 18 and 6
OC. 16 and 8
OD. 10 and 14
Let x be the number of apples in the first box and y be the number of apples in the second box. We can set up a system of two equations based on the information given:
x + y = 24 (equation 1)
x + y + 4 = 20 (equation 2)
Solving equation 2 for x + y, we get:
x + y = 16
Substituting this into equation 1, we get:
16 = 24
y = 8
Substituting y = 8 into equation 1, we get:
x + 8 = 24
x = 16
Therefore, the initial numbers of apples in the first and second boxes were 16 and 8, respectively. The answer is (OC) 16 and 8.
Let's assume that the initial number of apples in the first box is represented by x.
Since we have a total of 24 apples in both boxes, the number of apples in the second box can be represented by 24 - x.
If we add 4 apples to the second box, the total changes to 20 apples. So we can set up the equation:
x + 4 + (24 - x) = 20
Simplifying the equation:
x + 4 + 24 - x = 20
28 - x = 20
Subtracting 28 from both sides:
- x = -8
Dividing by -1:
x = 8
Therefore, the initial number of apples in the first box is 8, and the initial number of apples in the second box is 24 - 8, which is 16.
So the correct answer is option C: 16 and 8.