5.2 Levels 6-7 practice set

Stepping Up to Levels 6-7

Levels 6 and 7 are where the ACT WorkKeys Applied Math assessment separates a mid-range score from a top score. The scenarios now bury the numbers you need inside extra information, ask you to combine three or more operations, and often require a conversion along the way. The math itself is still arithmetic; there is no algebra beyond setting up a proportion, but the setup demands discipline. Work slowly, label every intermediate result, and never round until the final step.

The five worked walkthroughs below cover the highest-value Level 6-7 problem types: payroll with overtime, area or volume tied to a per-unit price, dilution and mixing ratios, best-buy unit-price comparisons, and production rates that cross a time conversion.

Payroll with overtime

Overtime pay is the single most common Level 6 workplace problem. The United States rule is time-and-a-half, meaning 1.5 times the base rate, for every hour worked beyond 40 in a week.

Worked example: A technician earns $18.00 per hour and worked 45 hours this week. What is her gross pay?

1. Split the hours: 40 regular + 5 overtime.
2. Regular pay: 40 x $18.00 = $720.00.
3. Overtime rate: 1.5 x $18.00 = $27.00 per hour.
4. Overtime pay: 5 x $27.00 = $135.00.
5. Add the two: $720.00 + $135.00 = $855.00.

The classic trap is multiplying all 45 hours by $18 (giving $810) and forgetting the premium on the extra 5 hours.

Area or volume with materials pricing

These items make you find a size first, then multiply by a price per unit.

Worked example (area and price): A warehouse floor is 40 ft by 25 ft and must be sealed with a coating that costs $0.90 per square foot. What is the total cost?

1. Area = length x width = 40 x 25 = 1,000 sq ft.
2. Cost = 1,000 x $0.90 = $900.00.

Worked example (volume and price): A planter box is 6 ft long, 3 ft wide, and 2 ft deep. Soil costs $4 per cubic foot. What does it cost to fill?

1. Volume = length x width x height = 6 x 3 x 2 = 36 cubic feet.
2. Cost = 36 x $4 = $144.00.

Dilution and mixing ratios

Ratio problems appear in cleaning, food service, and lab work. The key is to count the total number of parts before you divide.

Worked example: A disinfectant is mixed 1 part concentrate to 4 parts water. How much concentrate is needed to fill a 20-gallon tank?

1. Total parts = 1 + 4 = 5.
2. Size of one part = 20 gallons / 5 = 4 gallons.
3. Concentrate = 1 part = 4 gallons, and water = 4 x 4 = 16 gallons.

Check the work: 4 + 16 = 20 gallons, which matches the tank size.

Best-buy unit pricing

Here you convert each option to a price per unit, then compare, and the smallest number wins.

Worked example: Which is cheaper per pound, a 5-lb bag of rice for $6.25 or a 12-lb bag for $14.40?

1. 5-lb bag: $6.25 / 5 = $1.25 per pound.
2. 12-lb bag: $14.40 / 12 = $1.20 per pound.
3. Since $1.20 is less than $1.25, the 12-lb bag is the better buy.

Always divide price by quantity, not quantity by price, and keep the same unit, such as per pound or per ounce, across every option you compare.

Production rates across a time conversion

Rate problems become Level 7 when the time units do not match and you must convert.

Worked example: A bottling line fills 180 bottles in 15 minutes. How many bottles will it fill in a 2-hour run?

1. Rate = 180 / 15 = 12 bottles per minute.
2. Convert the time: 2 hours = 120 minutes.
3. Output = 12 x 120 = 1,440 bottles.

Multi-step checklist

• List the givens before doing anything, so extra numbers in the story do not distract you.
• Do the hidden conversion (minutes to hours, feet to yards, quarts to gallons) right where it belongs, not at the end.
• Keep a running label on every line: "$27/hr," "1,000 sq ft," "4 gallons." Labels catch setup errors early.
• Round only once, at the end, and only to the precision the question asks for, usually the nearest cent.
• Sanity-check the size of the answer: gross pay above the plain 40-hour amount, a best buy below the other prices, a diluted volume larger than the concentrate alone.

Reference summary

Take the five questions below at a Level 6-7 pace: expect three or more steps each, write down every intermediate value, and confirm the units before you commit to an answer. If a result looks too clean or far too large, retrace your setup rather than trusting the calculator display.