Granola Bar Order: Discount Threshold vs. Flat Shipping
A school store needs granola bars for a three-day event and expects to hand out 360 bars. Supplier A sells boxes of 24 bars at $0.68 per bar and takes 12% off the entire order once the order reaches 300 bars or more; shipping is included. Supplier B sells boxes of 20 bars at $15.90 per box and charges a flat $18 shipping fee no matter how many boxes are ordered. Boxes cannot be split, and the store will not buy fewer bars than it needs, though it may buy more if that lowers the total bill. The store's budget is $250 before tax, and the local sales tax rate is 6%, applied to the merchandise total plus shipping.
1. Which supplier gives the lower total cost for 360 bars, and by how much? Show the order size, discount status, and shipping for each.
Read the worked answer
Supplier A: 360 ÷ 24 = 15 boxes exactly. Cost = 360 × $0.68 = $244.80. Because 360 ≥ 300, the 12% discount applies: $244.80 × 0.88 = $215.42 (215.424). Shipping is included.
Supplier B: 360 ÷ 20 = 18 boxes exactly. Merchandise = 18 × $15.90 = $286.20. Add $18 shipping = $304.20.
Difference: $304.20 − $215.42 = $88.78 cheaper at Supplier A.
The trap is comparing $0.68 to $15.90/20 = $0.795 without applying the discount threshold and the flat shipping fee, which together swing the answer by nearly $90.
2. The event is scaled back to 288 bars. Does the cheaper supplier change? Justify with numbers.
Read the worked answer
Supplier A: 288 ÷ 24 = 12 boxes exactly, so 288 bars × $0.68 = $195.84. But 288 < 300, so the 12% discount does not apply.
Supplier B: 288 ÷ 20 = 14.4 boxes, and boxes cannot be split, so 15 boxes must be bought = 300 bars. Merchandise = 15 × $15.90 = $238.50, plus $18 shipping = $256.50.
Result: Supplier A is still cheaper, now by $256.50 − $195.84 = $60.66.
Note the two judgement points: dropping below 300 bars costs A its discount (the per-bar price effectively rises from $0.598 to $0.68), and B forces a round-up that produces 12 unneeded bars.
3. A volunteer claims that because of the 12% discount, the store could afford 480 bars under the $250 pre-tax budget. Evaluate the claim and state the largest workable order at Supplier A.
Read the worked answer
Test 480 bars at A: 480 × $0.68 = $326.40; with the discount, $326.40 × 0.88 = $287.23, which exceeds the $250 budget. The claim is false.
Find the actual limit: the discounted per-bar price is $0.68 × 0.88 = $0.5984. Budget ÷ price = $250 ÷ $0.5984 ≈ 417.8 bars, but orders must be whole boxes of 24.
- 17 boxes = 408 bars: 408 × $0.68 = $277.44 → × 0.88 = $244.15 ✔ under budget
- 18 boxes = 432 bars: 432 × $0.68 = $293.76 → × 0.88 = $258.51 ✘ over budget
So the largest workable order is 408 bars (still ≥ 300, so the discount does apply).
4. For the 360-bar order from Supplier A, does the total including 6% sales tax stay within the $250 budget?
Read the worked answer
Taxable amount at A is the merchandise total only, since shipping is included: $215.42.
Tax = $215.42 × 0.06 = $12.925 ≈ $12.93. Total = $215.42 + $12.93 = $228.35.
$228.35 ≤ $250, so the order fits the budget with about $21.65 to spare. (For contrast, Supplier B's taxable base includes shipping: $304.20 × 1.06 = $322.45, well over budget.) The judgement here is remembering that the discount is applied before tax, not after.