Mathematical Problem Solving Techniques

The video tutorial covers solving various math problems, including maximizing the value of y in a linear equation, calculating the time for two machines to produce a set number of bolts, finding the decimal equivalent of a fraction raised to a power, simplifying a mathematical expression, determining the selling price of batteries with a percentage increase, and calculating the sum of consecutive integers. Each problem is broken down step-by-step to enhance understanding.

In the equation y = 248 - 398x, which value of x will result in the highest value of y?

• 2

• -1

• 1

• 0

If Machine A produces 3 bolts per second and Machine B produces 5 bolts per second, how long will it take for both machines to produce 200 bolts together?

• 20 seconds

• 35 seconds

• 30 seconds

• 25 seconds

What is the decimal equivalent of (1/5)^5?

• 0.00032

• 0.0032

• 0.032

• 0.32

Simplify the expression: (90 - 8 * (20 / 4)) / (1/2). What is the result?

• 125

• 100

• 75

• 50

A dealer bought 100 batteries for a total of q dollars. If each battery is sold at 50% above the original cost, what is the selling price of each battery in terms of q?

• q/100

• 2q/150

• 3q/200

• 1.5q/100

In a sequence of ten consecutive integers, the sum of the first five is 560. What is the sum of the last five integers?

• 580

• 585

• 590

• 595