Question

Harper had $35 in her purse and found x dollars more on the couch. Cole had $41 in his wallet and spent twice as much money as Harper found on the couch. How much money did Harper find if both children had the same total amount of money?

Answer 1

By setting up an equation and solving for x, we find that Harper found $2 on the couch which, when added to her original $35, equals Cole's total after spending $4 (twice the $2 Harper found).

Step-by-step explanation:

We start with Harper having $35 in her purse and finding x dollars on the couch. Then, Cole has $41 and spent 2x dollars, which is twice the money that Harper found. Both end up with the same total amount of money.

To solve this problem, we set up an equation. Harper's total money is 35 + x dollars, and Cole's total money after spending is 41 - 2x dollars. Since they have the same total, we can write:

35 + x = 41 - 2x

We then solve for x:

1. Add 2x to both sides: 35 + x + 2x = 41 - 2x + 2x
2. Simplify: 35 + 3x = 41
3. Subtract 35 from both sides: 3x = 41 - 35
4. Simplify: 3x = 6
5. Divide both sides by 3: x = 2

Therefore, Harper found $2.

Answer 2

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.