Production Rates and Investment Growth

The video tutorial covers five math problems, each focusing on different mathematical concepts. Problem 124 deals with car sales distribution, using fractions to determine the number of sedans and station wagons sold. Problem 125 explores fraction inversion and comparison to identify values greater than one. Problem 126 calculates the combined work rate of two machines working together. Problem 127 analyzes mailing costs for separate and combined packages, while Problem 128 estimates investment growth using the rule of 70 for interest compounding. Each problem is solved step-by-step, demonstrating mathematical reasoning and algebraic manipulation.

If 1/3 of the cars sold were sedans and 1/5 of the remaining cars were station wagons, how many sedans were sold if N station wagons were sold?

• 2/3 N

• N

• 5/2 N

• 3/2 N

Given that p/q is less than 1, which of the following must be greater than 1?

• p+q

• q/p

• p-q

• p/q

If p/q is less than 1, what can be said about q/p?

• q/p is greater than 1

• q/p is less than 1

• q/p is negative

• q/p is equal to 1

Two machines work together to complete a task. Machine 1 takes 4 hours and Machine 2 takes 3 hours. How long will it take both machines working together to complete the task?

• 1 hour

• 12/7 hours

• 7/12 hours

• 2 hours

What is the combined rate of two machines if one produces 1/4 order per hour and the other 1/3 order per hour?

• 1/12 order per hour

• 7/12 order per hour

• 1/7 order per hour

• 12/7 order per hour

If a machine completes 1 order in 4 hours, what is its rate of production per hour?

• 1/3 order per hour

• 1/4 order per hour

• 1 order per hour

• 1/2 order per hour

If mailing a 3-pound and a 5-pound package separately costs 2x + 6y, and combined costs x + 7y, which method is cheaper?

• Separate is cheaper by y - x

• Combined is cheaper by x - y

• Combined is cheaper by y - x

• Separate is cheaper by x - y

If x is greater than y, what is the cost difference when mailing two packages separately versus combined?

• x + y

• x - y

• y - x

• 2x + 7y

If an investment doubles every 70/r years at r% interest, how long will it take to double at 8% interest?

• 9 years

• 8.75 years

• 10 years

• 7 years

How much will an investment of $5,000 grow to in 18 years at 8% interest compounded annually?

• $25,000

• $20,000

• $10,000

• $15,000