Final answer:
Rachel initially had 124 buttons, calculated by starting with the final number of buttons, subtracting the ones she gave away, and adding the new ones she got. However, this answer is not listed in the provided choices, indicating a possible issue with the provided information or question choices.
Step-by-step explanation:
To determine how many buttons Rachel had to start with, we can use the information provided in the question. She ended up with 136 buttons after giving away some and receiving some. The problem can be solved with a simple equation:
Starting buttons + 19 (received) - 7 (given away) = 136 (final amount)
Let's denote the number of starting buttons as 'x'.
x + 19 - 7 = 136
Now, let's solve for 'x':
x + 12 = 136
x = 136 - 12
x = 124
Therefore, Rachel started with 124 buttons.
Reading the question's answer choices, however, we can see that 124 is not listed, which means we may need to verify the addition or subtraction in our calculation.