Adam and Bob went apple picking in an orchard. At the end of the day, they realized that if Adam had picked 50 more apples, he would have picked twice as many as Bob picked. On the other hand, if Bob had picked 50 more apples, he would have picked twice as many as Adam picked.
How many apples did Adam and Bob pick all together?
a+50 = 2b
b+50 = 2a
(a+b)+100 = 2(a+b)
a+b = 100
To find the number of apples that Adam and Bob picked all together, we need to set up a system of equations based on the given information. Let's assume that Adam picked A apples and Bob picked B apples.
According to the first statement, if Adam had picked 50 more apples, he would have picked twice as many as Bob, so we can write the equation:
A + 50 = 2B
According to the second statement, if Bob had picked 50 more apples, he would have picked twice as many as Adam, so we can write the equation:
B + 50 = 2A
Now, we can solve this system of equations to find A and B.
Let's start by solving the first equation for A:
A = 2B - 50
Substitute this value of A into the second equation:
B + 50 = 2(2B - 50)
B + 50 = 4B - 100
3B = 150
B = 50
Now substitute the value of B back into the first equation to find A:
A = 2(50) - 50
A = 100 - 50
A = 50
Therefore, Adam picked 50 apples and Bob picked 50 apples.
To find the total number of apples they picked all together, add their individual quantities:
Total = Adam's apples + Bob's apples
Total = 50 + 50
Total = 100
So, Adam and Bob together picked 100 apples.