Personal Financial Literacy>Analyzing and Comparing Monetary Incentives(TEKS.Math.7.13.F)
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Texas 7th Grade Math › Personal Financial Literacy>Analyzing and Comparing Monetary Incentives(TEKS.Math.7.13.F)
You are buying 3 identical water bottles that cost 20 dollars each (total 60 dollars). Four stores advertise these promotions:
- Store A: 25% off all items
- Store B: Buy 2, get 1 free
- Store C: 10 dollars off purchases over 40 dollars
- Store D: 30% off one item only Which incentive saves the most money on this purchase?
Store A
Store B
Store C
Store D
Explanation
Compute savings on a 60-dollar purchase of three 20-dollar items:
- Store A: 25% of 60 dollars is $0.25 \times 60 = 15$ dollars saved.
- Store B: Buy 2, get 1 free means you pay for only 2 items: save 20 dollars.
- Store C: 10 dollars off over 40 dollars is 10 dollars saved.
- Store D: 30% off one item is $0.30 \times 20 = 6$ dollars saved. The greatest savings is 20 dollars at Store B. Decision factors: Buy-2-get-1-free works best when you buy in multiples of three; percent-off applies even if you buy fewer or more items.
You are buying 2 identical headphones priced at 80 dollars each (total 160 dollars). Choose the best promotion:
- Option A: 30% off one item of your choice
- Option B: Buy 1, get the 2nd for 40% off
- Option C: 10% off the whole purchase plus a 10-dollar mail-in rebate per headphone (limit 2)
- Option D: 20 dollars off when you spend 100 dollars or more Which option gives the greatest total savings?
Option A: 30% off one item
Option B: Second at 40% off
Option C: 10% off entire purchase + 10-dollar rebate per item
Option D: 20 dollars off 100 dollars+
Explanation
Regular total is $2 \times 80 = 160$ dollars.
- A: Save $0.30 \times 80 = 24$ dollars.
- B: Save 40% on one item: $0.40 \times 80 = 32$ dollars saved.
- C: Save $0.10 \times 160 = 16$ dollars now, plus rebates: $2 \times 10 = 20$ dollars later; total savings 36 dollars.
- D: Qualifies for 20 dollars off; save 20 dollars. Greatest savings is Option C (36 dollars). Decision factors: rebates reduce your net cost but arrive later and require submission; percent-off applies immediately; check rebate limits.
An online store sells notebooks for 18 dollars each. You plan to buy 3. Shipping is 8 dollars unless the pre-discount merchandise total is at least 60 dollars (then shipping is free). Four promotions are available:
- P1: 20% off your order (shipping charged normally)
- P2: Buy 3, get free shipping only (no item discount)
- P3: 12 dollars off when you spend 60 dollars or more (based on pre-discount total; you may add a 6-dollar filler item to reach 60)
- P4: 15% off your order and shipping capped at 4 dollars Which promotion leads to the lowest total cost for this purchase?
P3: Add a 6-dollar filler to reach 60; take 12 dollars off; free shipping
P1: 20% off; pay 8 dollars shipping
P2: Buy 3; free shipping only
P4: 15% off; shipping capped at 4 dollars
Explanation
Base merchandise total: $3 \times 18 = 54$ dollars.
- P3: Add a 6-dollar item to reach 60 dollars pre-discount ⇒ free shipping. Discount 12 dollars ⇒ total $60 - 12 = 48$ dollars, shipping 0 ⇒ 48 dollars total.
- P1: 20% off 54 is $0.20 \times 54 = 10.80$ saved ⇒ $54 - 10.80 = 43.20$ dollars; add 8 shipping ⇒ 51.20 dollars total.
- P2: Free shipping only ⇒ 54 dollars total.
- P4: 15% off 54 is $0.15 \times 54 = 8.10$ saved ⇒ $54 - 8.10 = 45.90$ dollars; shipping 4 ⇒ 49.90 dollars total. Lowest total is 48 dollars with P3. Decision factors: thresholds are usually based on pre-discount totals; adding a small item can unlock a better discount and free shipping if the net drops more than the filler's cost.
A car has a price of 25,000 dollars. You can choose one of these incentives for a 5-year loan:
- Offer 1: 2,000 dollars cash back; finance the reduced price at 4.5% APR
- Offer 2: 0.9% APR financing (no cash back) Using simple interest to estimate total interest over 5 years, which offer costs less overall?
Take 2,000 dollars cash back and finance at 4.5% APR
Take 0.9% APR for 5 years with no cash back
Take both offers
Neither—both cost the same
Explanation
Estimate with simple interest (for comparison only):
- Offer 1: Price after cash back is $25{,}000 - 2{,}000 = 23{,}000$ dollars. Interest ≈ $23{,}000 \times 0.045 \times 5 = 5{,}175$ dollars. Total ≈ $23{,}000 + 5{,}175 = 28{,}175$ dollars.
- Offer 2: No cash back; principal 25,000 dollars. Interest ≈ $25{,}000 \times 0.009 \times 5 = 1{,}125$ dollars. Total ≈ $25{,}000 + 1{,}125 = 26{,}125$ dollars. Offer 2 costs about 2,050 dollars less. Decision factors: exact loan costs use amortized payments (not simple interest); lower APR usually means lower monthly payments; consider eligibility, fees, and whether you can use the cash back better elsewhere.