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Jordan and Jake each work during the summer. Jordan earns $9 per hour at her job. Jordan also gets a $10 weekly allowance.

Jordan displayed her earnings in a table.

Hours 0 1 2 3 4 5 6 7 8
Earnings 10 19 28 37 46 55 64 73 82
Jake earns $6.50 per hour at his job. Jake also gets a $15 weekly allowance.

Jake displayed his earnings in a graph.

How many hours will it take for Jordan and Jake to earn the same amount of money?

Enter your answer in the box.

hours

1 answer

To find out how many hours it will take for Jordan and Jake to earn the same amount of money, we can set up equations for each of their earnings.

Jordan's Earnings:

  • Hourly wage: $9 per hour
  • Weekly allowance: $10

Let \( h \) represent the number of hours worked. Jordan's total earnings can be expressed as: \[ E_J = 9h + 10 \]

Jake's Earnings:

  • Hourly wage: $6.50 per hour
  • Weekly allowance: $15

Jake's total earnings can also be expressed as: \[ E_k = 6.5h + 15 \]

Now we can set their earnings equal to each other to find out when they earn the same amount: \[ 9h + 10 = 6.5h + 15 \]

Now, let's solve for \( h \):

  1. Subtract \( 6.5h \) from both sides: \[ 9h - 6.5h + 10 = 15 \] \[ 2.5h + 10 = 15 \]

  2. Subtract 10 from both sides: \[ 2.5h = 5 \]

  3. Divide both sides by 2.5: \[ h = \frac{5}{2.5} = 2 \]

Thus, it will take 2 hours for Jordan and Jake to earn the same amount of money.

The answer is: \[ \boxed{2} \]