A line graph shows the cumulative savings of Ahmad and Siti over several weeks. At the end of Week 4, Ahmad has saved $80 and Siti has saved $60. Ahmad saves $15 each week and Siti saves $20 each week. Both continue saving at these fixed amounts. After how many more weeks from Week 4 will Siti have saved more than Ahmad for the first time?
Show Worked Solution
Worked Solution
Step 1: Write expressions for each person's savings after n more weeks.
Ahmad: $80 + $15n
Siti: $60 + $20n
Step 2: Find when Siti first has MORE than Ahmad.
60 + 20n > 80 + 15n
20n - 15n > 80 - 60
5n > 20
n > 4
Step 3: The smallest whole number of weeks greater than 4 is 5.
Step 4: Verify.
After 5 weeks: Ahmad = $80 + $75 = $155; Siti = $60 + $100 = $160. Siti leads. ✓
After 4 weeks: Ahmad = $80 + $60 = $140; Siti = $60 + $80 = $140. Equal (not yet more). ✓
Answer: 5 weeks after Week 4.
Correct answer: 5 weeks
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