Discount and Tax on a Bulk Purchase
A school buys 24 identical calculators listed at $18.75 each. The supplier offers a 15% discount on the subtotal for orders of 20 or more units. After the discount, a 6% sales tax is applied to the discounted subtotal. The business office has budgeted $400 for the purchase and needs to know whether the budget covers the final total. A clerk computes the total by taking 15% off, then adding 6% tax, but rounds the discounted subtotal to the nearest dollar before applying tax - a step the office worries may push the result off. The office wants the exact final total to the cent and a clear statement of whether $400 is enough.
1. Compute the exact final total: subtotal, discount amount, discounted subtotal, tax, and grand total.
Read the worked answer
Subtotal: 24 × $18.75 = $450.00.
Discount: 15% of $450 = 0.15 × 450 = $67.50. Discounted subtotal = 450 − 67.50 = $382.50.
Tax: 6% of $382.50 = 0.06 × 382.50 = $22.95.
Grand total = 382.50 + 22.95 = $405.45.
Check discount another way: paying 85% of subtotal = 0.85 × 450 = $382.50. Tax factor 1.06: 382.50 × 1.06 = $405.45. Consistent.
2. Does the $400 budget cover the purchase? State the shortfall or surplus.
Read the worked answer
Grand total $405.45 vs. budget $400.
Shortfall = 405.45 − 400 = $5.45.
The budget does NOT cover the purchase; the office is $5.45 over. Options: reduce quantity, negotiate, or request a small budget increase. Note the shortfall is small relative to the total (~1.3%), so a minor adjustment suffices.
3. The clerk rounds the discounted subtotal ($382.50) to $383 before taxing. What total does the clerk get, and how far is it from the exact total?
Read the worked answer
Clerk's tax: 6% of $383 = 0.06 × 383 = $22.98. Clerk's total = 383 + 22.98 = $405.98.
Exact total = $405.45. Difference = 405.98 − 405.45 = $0.53 over.
Rounding the subtotal up by $0.50 inflated the tax by about 6% of $0.50 = $0.03 and the total by $0.53. The exact figure ($405.45) is the one to use; both totals still exceed $400, so the budget conclusion is unchanged, but the cent-level figure matters for accounting.