Side Hustle Showdown Activity
Algebra 1 Real-World Lab Systems & Equivalence
SIDE HUSTLE SHOWDOWN
Solving Multi-Step Equations with Variables on Both Sides
Name:
Date:
Period:
Mission Briefing: Four pairs of student entrepreneurs are launching competing side ventures. Your task is to set up and solve multi-step equations to locate the exact break-even point where both options earn or cost the exact same amount.
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Case 01: The Lawn Care Equipment Clash
Basic Variables on Both Sides
Plan A: GreenThumb Crew
Buys commercial gear for $210 upfront, then charges clients $25 per lawn mowed.
Net: 25m - 210
Plan B: TurboTurf Co.
Rents lighter equipment for $50 upfront, but charges only $15 per lawn mowed.
Net: 15m - 50
a) Set up the equation where GreenThumb's net profit equals TurboTurf's net profit (let m = lawns):
Equation: ___________________________________________________________
b) Solve step-by-step for m:
Show balance steps here...
Final Answer: m = ______ lawns
Decision Check: If the season brings 20 lawns, which crew earns more profit? Choice: __________________
2
Case 02: Custom Merch Supply Deal
Distributive Property (One Side)
Maya and Noah are ordering blank hoodies for their school club merchandise store.
Supplier X (Local Print Hub)
Charges $14 per hoodie, plus a fixed screen setup fee of $48.
Cost: 14h + 48
Supplier Y (Bulk District Press)
Offers bundled packs where each pack of hoodies has a special discount: 2(4h + 42).
Cost: 2(4h + 42)
a) Write the break-even equation: 14h + 48 = 2(4h + 42)
b) Apply the Distributive Property and show each inverse operation to isolate h:
Step 1: Distribute
Step 2: Collect Variables
Step 3: Solve for h
Break-Even Quantity: h = ______ hoodies
Verification: Substitute your answer back into both suppliers' formulas to prove the total costs are identical.
Part II
SIDE HUSTLE SHOWDOWN • ADVANCED CONTRACTS
Distributive Property & Like Terms on Both Sides
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Case 03: The Mobile DJ Gig Battle
Double Distributive Property
Two competing event entertainment companies price their lighting, sound packages, and hourly technician rates using tiered contracts:
SonicBoom Audio:
3(4x + 12)
3 zones of 4 hrs sound + $12 staging
BassDrop Events:
2(3x + 36)
2 modular trailers of 3 hrs + $36 bass fee
Solve for x (the base hourly gig rate) where both bookings bill identically:
1. Expand both sides using distributive property:
2. Move variable terms to one side:
3. Isolate x using inverse operations:
Check: 3(4·___ + 12) = 2(3·___ + 36) x = $_______ / hour
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Case 04: The Downtown Food Truck Faceoff
Distribution + Combining Like Terms
Two gourmet food trucks at the town festival calculate their daily gross profit based on combo boxes sold (c). Their financial models include coupon promos and staffing adjustments:
4(2c + 5) - 3c = 3(c + 14) + 10
Left Side (Smash Burger Truck):
Expand 4(2c + 5) and combine with -3c.
Right Side (Taco Fiesta Truck):
Expand 3(c + 14) and combine with +10.
Show complete algebraic steps to find the break-even volume c:
Show intermediate equations after simplifying both sides:
Total Revenue at break-even: $___________ c = ______ combo boxes
Chief Financial Officer (CFO) Strategy Challenge
In Case 01, TurboTurf has a lower startup cost ($50 vs $210), but GreenThumb makes a higher profit per lawn ($25 vs $15). Explain in your own words how solving a multi-step equation reveals which business model is superior for a short summer (few lawns) versus a long summer (many lawns).
