Mathematics Flashcards

A contractor mixes concrete using a ratio of cement : sand : gravel = 1 : 2.5 : 3.5. If the total batch must weigh exactly 980 pounds, how many pounds of sand are needed?

Answer: 350 pounds

The ratio parts total 1 + 2.5 + 3.5 = 7 parts. Each part equals 980 ÷ 7 = 140 pounds. Sand is 2.5 parts, so 2.5 × 140 = 350 pounds.

A rectangular storage tank measures 8 feet long, 5 feet wide, and 4 feet tall. It is currently 37.5% full of water. How many cubic feet of water does it contain?

Answer: 60 cubic feet

Total volume = 8 × 5 × 4 = 160 cubic feet. 37.5% of 160 = 0.375 × 160 = 60 cubic feet.

Solve for x: 5x − 3(x − 4) = 2x + 12

Answer: Infinitely many solutions (identity)

Distribute: 5x − 3x + 12 = 2x + 12 → 2x + 12 = 2x + 12. Subtracting 2x from both sides gives 12 = 12, which is always true. This is an identity, so every real number is a solution.

A pump drains a tank at 15 gallons per minute. A second pump simultaneously fills the same tank at 9 gallons per minute. If the tank holds 360 gallons and starts full, how many minutes will it take to empty the tank with both pumps running?

Answer: 60 minutes

The net drain rate is 15 − 9 = 6 gallons per minute. Time to empty = 360 ÷ 6 = 60 minutes.

What is the result when you subtract −4.75 from −1.25?

Answer: 3.50

Subtracting a negative is the same as adding the positive: −1.25 − (−4.75) = −1.25 + 4.75 = 3.50.

A worker earns $18.40 per hour and receives time-and-a-half for all hours beyond 40 in a week. The worker logs 47 hours. What is the gross weekly pay?

Answer: $929.20

Regular pay: 40 × $18.40 = $736.00. Overtime rate: $18.40 × 1.5 = $27.60/hr. Overtime pay: 7 × $27.60 = $193.20. Total: $736.00 + $193.20 = $929.20.