PSA Math Probe #4

Basic Measurement (Whole Numbers)

A police officer needs to describe a suspect's height. If the suspect is 5 feet 9 inches tall, how many total inches is that?

Answer explanation

Solution: (5 × 12) + 9 = 69 inches

Method: Convert feet to inches by multiplying by 12, then add remaining inches

Tape Measurement (Fractions)

At a crime scene, you measure the distance between two pieces of evidence. The tape measure shows 3¾ feet. How many inches is this?

Answer explanation

• Solution: (3 × 12) + (¾ × 12) = 36 + 9 = 45 inches

• Method: Convert whole feet to inches, then convert the fraction of feet to inches

Ratios (Emergency Response)

Safety regulations require 2 lifeguards for every 15 swimmers. How many lifeguards are needed for 60 swimmers?

Answer explanation

Solution: 2:15 = x:60

Cross multiply: 15x = 2 × 60

x = 120 ÷ 15 = 8 lifeguards needed

Method: Set up a proportion and solve for unknown

Percentages (Incident Reports)

Out of 150 emergency calls last week, 40% were traffic accidents. How many traffic accident calls were there?

Answer explanation

Solution: 150 × 0.40 = 60 calls

Method: Convert percentage to decimal (40% = 0.40) and multiply

Decimals (Budget)

Your unit has $2,345.50 in its supplies budget. After spending $978.75, how much remains?

Answer explanation

Solution: $2,345.50 - $978.75 = $1,366.75

Method: Align decimal points and subtract

Proportions (Staff Planning)

If 6 security officers can patrol 2 buildings in 8 hours, how many officers are needed to patrol 5 buildings at the same time?

Answer explanation

Solution: 6:2 = x:5

Cross multiply: 2x = 6 × 5

x = 30 ÷ 2 = 15 officers

Method: Set up proportion and solve

Practical Geometry (Scene Documentation)

A rectangular crime scene measures 15 feet by 25 feet. What is the area that needs to be secured?

Answer explanation

Solution: Area = length × width

15 × 25 = 375 square feet

Method: Apply the area formula for a rectangle

Practical Algebra (Response Time)

If a fire truck travels 45 miles per hour, how long will it take to reach an emergency 15 miles away?

Answer explanation

Solution: Time = Distance ÷ Speed

15 ÷ 45 = 0.333 hours = 20 minutes

Method: Use time = distance/speed formula, and convert to minutes

Mixed Numbers (Equipment Weight)

A firefighter carries 2½ pounds of tools in each hand. What is the total weight being held?

Answer explanation

Solution: 2½ + 2½ = 5 pounds

Method: Add mixed numbers by combining whole numbers and fractions

Fractions and Decimals (Medical Dosage)

An EMT needs to give a patient ¾ of a standard dose. If the standard dose is 2.5 mL, how much should they give?

Answer explanation

Solution: ¾ × 2.5 = 1.875 mL

Method: Convert fraction to decimal (0.75) and multiply