To determine how many hours it will take for Jordan and Jake to earn the same amount of money, we need to set up equations for their earnings and solve for the number of hours where these earnings are equal.
First, we establish Jordan's earnings equation. Jordan earns \[tex]$59 per hour and gets a \$[/tex]10 weekly allowance. Therefore, her earnings (E_Jordan) as a function of hours (h) can be written as:
[tex]\[ E_{\text{Jordan}} = 59h + 10 \][/tex]
Next, we set up Jake's earnings equation. Jake earns \[tex]$650 per hour and gets a \$[/tex]15 weekly allowance. Thus, his earnings (E_Jake) as a function of hours (h) can be expressed as:
[tex]\[ E_{\text{Jake}} = 650h + 15 \][/tex]
We want to find the number of hours (h) where their earnings are equal. Therefore, we set the two equations equal to each other:
[tex]\[ 59h + 10 = 650h + 15 \][/tex]
To isolate [tex]\(h\)[/tex], we first move all terms involving [tex]\(h\)[/tex] to one side of the equation and constant terms to the other side:
[tex]\[ 59h - 650h = 15 - 10 \][/tex]
Combine like terms:
[tex]\[ -591h = 5 \][/tex]
Next, solve for [tex]\(h\)[/tex] by dividing both sides of the equation by [tex]\(-591\)[/tex]:
[tex]\[ h = \frac{5}{-591} \][/tex]
Thus, the number of hours it will take for Jordan and Jake to earn the same amount of money is:
[tex]\[ h = -\frac{5}{591} \][/tex]
This essentially means that it's not feasible within regular working hours since they cannot practically work a negative number of hours. However, mathematically this is the solution to when their earnings would meet under the given constraints.
