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Difficulty: Very hardDecimal Operations and Currency Word Problems

A logistics company is purchasing diesel fuel for its fleet. The base price of diesel is $4.50\$4.50 per gallon. The company uses a corporate discount card that provides a $0.30\$0.30 per gallon reduction on the first 120120 gallons, and a 20%20\% discount off the base price for any additional gallons purchased beyond the first 120120.

The company purchases a total of 250250 gallons of diesel.

After calculating the cost of the fuel with the discounts applied, a federal excise tax of $0.40\$0.40 per gallon is added for the entire purchase volume. Finally, a 5%5\% state sales tax is applied to the subtotal (the subtotal includes both the discounted fuel cost and the excise tax).

If the company pays for the entire transaction using a prepaid account that currently has a balance of $1,500.00\$1,500.00, what will be the remaining balance in dollars after the purchase?

Answer: 374.4 $

Answer

374.40
The correct answer is found by first calculating the tiered fuel costs: $504.00\$504.00 for the first 120 gallons (at $4.20\$4.20/gal) and $468.00\$468.00 for the remaining 130 gallons (at $3.60\$3.60/gal). Adding the $100.00\$100.00 federal excise tax gives a subtotal of $1072.00\$1072.00. The 5%5\% state tax is calculated on this subtotal, adding $53.60\$53.60 for a final cost of $1125.60\$1125.60. Subtracting this from the $1500.00\$1500.00 account balance leaves $374.40\$374.40.

Step-by-Step Solution

1
Calculate the fuel cost for the first tier (120 gallons).
$504.00
The first 120 gallons receive a 0.30flatdiscount.Thepricepergallonis0.30 flat discount. The price per gallon is 4.50 - 0.30=0.30 = 4.20. Multiplying 120 by 4.20gives4.20 gives 504.00.
2
Calculate the fuel cost for the second tier (remaining gallons).
$468.00
There are 250 - 120 = 130 remaining gallons. A 20% discount on 4.50givesapriceof4.50 gives a price of 3.60 per gallon. Multiplying 130 by 3.60gives3.60 gives 468.00.
3
Find the total discounted fuel cost before taxes.
$972.00
Add the costs of both tiers together: 504.00+504.00 + 468.00 = $972.00.
4
Calculate the federal excise tax.
$100.00
The excise tax applies to all 250 gallons at 0.40pergallon.Multiplying250by0.40 per gallon. Multiplying 250 by 0.40 gives $100.00.
5
Calculate the subtotal and the state sales tax.
$53.60
The subtotal is 972.00(fuel)+972.00 (fuel) + 100.00 (excise) = 1072.00.The51072.00. The 5% state tax on this subtotal is 1072.00 * 0.05 = $53.60.
6
Find the final transaction cost.
$1125.60
Add the state sales tax to the subtotal: 1072.00+1072.00 + 53.60 = $1125.60.
7
Calculate the remaining balance in the prepaid account.
$374.40
Subtract the total transaction cost from the starting balance: 1500.00−1500.00 - 1125.60 = $374.40.

Key Concept

Solving multi-step financial word problems involving tiered discounts, dual tax application sequences, and balance deductions.
Estimated Time:3m 0s
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Topics

Decimal Operations and Currency Word Problems

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