Final answer:
To calculate the number of weeks it took Jacinta to earn $450 more than Jose, we need to calculate their weekly earnings and set up an equation. It took Jacinta 130 weeks to earn $450 more than Jose.
Step-by-step explanation:
To calculate the number of weeks it took Jacinta to earn $450 more than Jose, we need to first calculate the weekly earnings for both Jose and Jacinta.
Jose earned $8 per hour and worked 8 hours a day for 5 days a week. So, his weekly earnings can be calculated as: $8 x 8 x 5 = $40 x 5 = $200.
Now, let's assume it took Jacinta 'x' number of weeks to earn $450 more than Jose. So, Jacinta's weekly earnings can be calculated as: ($200 + $450) ÷ x = $650 ÷ x.
We know that Jacinta earned an 8-hour day for 5 days a week, so her total weekly earnings can be calculated as: 8 x 5 x ($650 ÷ x) = 40 x ($650 ÷ x) = $26000 ÷ x.
Now, we can set up an equation to find the value of 'x'.
$26000 ÷ x = $200
Cross multiply and solve for 'x': $26000 = $200x
x = $26000 ÷ $200
x = 130.
Therefore, it took Jacinta 130 weeks to earn $450 more than Jose.