Final answer:
Harper found $2 on the couch. This was determined by setting up an equation to equalize the final amount of money Harper and Cole had, and solving for the variable 'x'.
Step-by-step explanation:
The student has asked a question related to simple algebra. Harper initially had $35 and found x dollars on the couch. Cole had $41 and spent twice the amount Harper found, which can be represented as 2x dollars. The condition given is that after these transactions, Harper and Cole have the same amount of money.
To find out how much Harper found, we set up an equation that represents the total amount of money each person has after the transactions. For Harper, she has her original $35 plus an unknown amount 'x'. For Cole, he starts with $41 but spends twice the amount Harper found, or '2x'.
So, Harper's total is: $35 + x
Cole's total after spending is: $41 - 2x
We equalize both totals because they end up with the same amount:
$35 + x = $41 - 2x
Now solve for 'x':
Add '2x' to both sides to get: 3x + $35 = $41
Subtract $35 from both sides to isolate 'x': 3x = $6
Divide both sides by 3 to solve for 'x':
x = $2
So, Harper found $2 on the couch.