To solve this problem, we can use a system of equations based on their savings over time.
Let �t be the number of months it will take for Jaclyn and Pedro to have saved the same amount of money.
Step 1: Set Up Equations for Both Jaclyn and Pedro For Jaclyn: Initial savings + Monthly earnings times the number of months = Total savings 120+40�=Total savings for Jaclyn120+40t=Total savings for Jaclyn
For Pedro: Initial savings + Monthly earnings times the number of months = Total savings 180+20�=Total savings for Pedro180+20t=Total savings for Pedro
Step 2: Set the Two Equations Equal to Each Other To find the time when both have the same savings: 120+40�=180+20�120+40t=180+20t
Step 3: Solve for �t Now, let’s solve the equation for �t to find out the number of months it will take for both to have the same savings.
Step 1: Set Up Savings Over Time for Both Jaclyn and Pedro
- For every month:
- Jaclyn saves: 120+40�120+40t
- Pedro saves: 180+20�180+20t
Step 2: Equate the Savings To find when both have the same amount saved: 120+40�=180+20�120+40t=180+20t
Step 3: Solve for �t By rearranging the equation: 20�=6020t=60 So, �=6020t=2060
Now, we’ll compute the value for �t.
After simplifying, we find that �=3t=3.
This means it will take 3 months for Jaclyn and Pedro to have saved the same amount of money, given they both save their entire allowances.