Adam and Bob went apple picking in an orchard. At the end of the day, they counted the number of apples they picked. They realized that if Adam picked 39 more apples, he would have picked twice as many as Bob picked. Also, if Bob picked 39 more apples, he would have picked twice as many as Adam picked. How many apples did Adam and Bob pick all together?
Adam --- x apples
Bob ---- y apples
x+39 = 2y or x - 2y = -39
2x = y + 39 or 2x - y = 39
the first equation: x - 2y = -39
double the 2nd : 4x - 2y = 78
subtract them:
3x = 117
x = 39
into the 2nd:
78 - y = 39
-y = -39
y = 39
They each picked 39 apples.
To solve this problem, let's call the number of apples Adam picked A and the number of apples Bob picked B. We are given two statements:
1) "If Adam picked 39 more apples, he would have picked twice as many as Bob picked." This can be written as A + 39 = 2B.
2) "If Bob picked 39 more apples, he would have picked twice as many as Adam picked." This can be written as B + 39 = 2A.
We can solve these two equations simultaneously to find the values of A and B.
Let's solve equation 1) for A:
A = 2B - 39
Now substitute this value of A in equation 2):
B + 39 = 2(2B - 39)
B + 39 = 4B - 78
3B = 117
B = 39
Now, substitute the value of B back into equation 1:
A = 2(39) - 39
A = 78 - 39
A = 39
So, Adam picked 39 apples and Bob picked 39 apples as well.
To find the total number of apples they picked all together, add Adam's and Bob's values:
39 + 39 = 78
Therefore, Adam and Bob picked a total of 78 apples.