Reconciling a Clinic Supply Order Against a Budget Line
A clinic office manager is reconciling a supply order before the fiscal quarter closes. The order includes 4 boxes of exam gloves at $12.75 per box, 6 boxes of gauze at $8.40 per box, and 2 cases of paper towels at $23.50 per case. The distributor applies a 10% discount to the subtotal when the subtotal exceeds $100, then adds a flat $9.95 shipping fee, and finally applies 6% sales tax to the discounted subtotal only (shipping is not taxed). The manager has a $200.00 budget line for this order and also wants to know the per-box cost of the gloves after the discount and tax are allocated in proportion to each line's share of the discounted subtotal. Any remaining budget must be reported to the finance office with the number of additional full boxes of gauze it could buy, using the same discount and tax rules.
1. What is the order total, and how much of the $200.00 budget line remains?
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Subtotal by line:
- Gloves: 4 × $12.75 = $51.00
- Gauze: 6 × $8.40 = $50.40
- Paper towels: 2 × $23.50 = $47.00
Subtotal = 51.00 + 50.40 + 47.00 = $148.40, which exceeds $100, so the discount applies.
Discount: 148.40 × 0.10 = $14.84, giving a discounted subtotal of $133.56.
Tax: 133.56 × 0.06 = $8.0136, rounded to $8.01.
Shipping: $9.95 (untaxed).
Total: 133.56 + 8.01 + 9.95 = $151.52.
Remaining budget: 200.00 − 151.52 = $48.48.
2. What is the true per-box cost of the exam gloves once discount and tax are allocated proportionally?
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Discounted glove line: 51.00 × 0.90 = $45.90.
Share of the discounted subtotal: 45.90 ÷ 133.56 = 0.3437, or about 34.37%.
Allocated tax: 0.3437 × 8.01 = $2.75 (check: 45.90 × 0.06 = 2.754, which matches, because tax is a flat 6% of each line).
Allocated glove cost: 45.90 + 2.75 = $48.65.
Per box: 48.65 ÷ 4 = $12.16.
Answer: about $12.16 per box, versus the $12.75 sticker price - roughly a 5% effective saving. Shipping was excluded because it is a flat fee tied to the shipment, not to the gloves.
3. How many additional full boxes of gauze can be added without exceeding the $200.00 budget line?
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The subtotal is already above $100, so any added gauze still receives the 10% discount and is taxed at 6%.
Effective cost per added box: 8.40 × 0.90 = $7.56; 7.56 × 1.06 = $8.0136, about $8.01.
Test against the remainder: 48.48 ÷ 8.01 = 6.05.
Check both sides: 6 boxes = 6 × 8.01 = $48.08, which fits. 7 boxes = 7 × 8.01 = $56.07, which exceeds $48.48 by about $7.59.
Answer: 6 additional boxes, leaving roughly $0.40 unspent. Shipping does not increase because the fee is flat, and the discount tier is unaffected because the subtotal only grows.