[Solution] Jaclyn has $120 saved and earns $40 each month in allowance. Pedro has $180 saved and earns $20 a month in allowance. If they both save their entire allowances, how long will it take before Jaclyn and Pedro have saved the same amount of money?
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.