Marcie started working a part-time job at the beginning of the summer. After four weeks, she increased the number of hours she worked each week by 1/5. After another four weeks, she decreased the number of hours she worked each week by 1/3. From then on, she worked 20 hours weekly. How many hours was she working each week when she began working at the beginning of the summer?
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Wait, I got 25 but I see 30 is an option. Let me recheck — after the decrease by 1/3 she works 20, so before that decrease it was 30, right? Then before the increase by 1/5 it was 25. Did I flip the order of the operations?
You're on the right track, just check which change happens first. The 1/5 increase comes before the 1/3 decrease.
Ah I see, I had the sequence backwards in my head. Thanks!
Took me a second to set this up but working backwards made it click. 20 = (2/3)x, so x = 30 before the decrease, then 30 = (6/5)y for the original.
This is the cleanest way to think about it, imo. Reverse the operations!
Is this really 555-605? I feel like the trick is just realizing you reverse the changes rather than applying them forward. Once you see it it's fast.
Yeah it's more of a reading-comprehension trap than a math one. The 1/3 decrease is what gets people.
Can someone explain why we don't just do 20 × 1/3 + 20 to undo the decrease? I keep getting a weird number that way.
Because a decrease of 1/3 means she's left with 2/3, not that 1/3 was removed from 20. Set it up as 2/3 of the previous = 20.
That distinction tripped me up too — 'decreased by 1/3' vs 'is 1/3 of.'
What it tests
Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.
Common trap
Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.