Examkin

Question

Difficulty: HardDecimal Operations and Currency Word Problems

A motor pool mechanic is comparing four bulk purchasing options for a specialized synthetic lubricant. To make the most cost-effective decision, they need to determine the actual cost per ounce for each option, accounting for any additional fees or discounts.

Arrange the following purchasing options in order from the lowest cost per ounce to the highest cost per ounce.

  1. 1Bravo Brand: 8.08.0 ounces for $33.20\$33.20 with no extra fees
  2. 2Delta Brand: 24.024.0 ounces for $102.00\$102.00 with no extra fees
  3. 3Alpha Brand: 12.512.5 ounces for $52.50\$52.50, plus a $1.25\$1.25 handling fee
  4. 4Charlie Brand: 15.015.0 ounces for $69.00\$69.00, minus a $3.00\$3.00 instant rebate

Answer

The correct sequence from lowest to highest cost per ounce is: Bravo Brand ($4.15\$4.15), Delta Brand ($4.25\$4.25), Alpha Brand ($4.30\$4.30), and Charlie Brand ($4.40\$4.40).
To accurately compare the purchasing options, each one must be reduced to its unit cost (price per ounce) after adjusting for all fees and rebates. Bravo Brand is the cheapest at $4.15\$4.15 per ounce. Delta Brand is next at $4.25\$4.25 per ounce. Alpha Brand follows at $4.30\$4.30 per ounce after factoring in its handling fee. Charlie Brand is the most expensive at $4.40\$4.40 per ounce even after applying the instant rebate.

Step-by-Step Solution

1
Calculate the unit cost for Alpha Brand.
$4.30\$4.30 per ounce.
First, find the total cost by adding the handling fee: $52.50+$1.25=$53.75\$52.50 + \$1.25 = \$53.75. Next, divide by the volume: $53.75÷12.5=$4.30\$53.75 \div 12.5 = \$4.30.
2
Calculate the unit cost for Bravo Brand.
$4.15\$4.15 per ounce.
Divide the total cost by the volume: $33.20÷8.0=$4.15\$33.20 \div 8.0 = \$4.15.
3
Calculate the unit cost for Charlie Brand.
$4.40\$4.40 per ounce.
First, find the total cost by subtracting the rebate: $69.00−$3.00=$66.00\$69.00 - \$3.00 = \$66.00. Next, divide by the volume: $66.00÷15.0=$4.40\$66.00 \div 15.0 = \$4.40.
4
Calculate the unit cost for Delta Brand.
$4.25\$4.25 per ounce.
Divide the total cost by the volume: $102.00÷24.0=$4.25\$102.00 \div 24.0 = \$4.25.
5
Order the calculated unit costs from lowest to highest.
Bravo Brand, Delta Brand, Alpha Brand, Charlie Brand.
Comparing the decimal values gives 4.15<4.25<4.30<4.404.15 < 4.25 < 4.30 < 4.40.

Key Concept

Calculating and comparing unit prices involving decimals, fees, and discounts.
Rate this question

Topics

Decimal Operations and Currency Word Problems

More questions from this topic