Mathematical Concepts and Problem Solving

The video tutorial covers three problems. Problem 77 involves calculating Miss Smith's income for 1991 using percentage increase and linear equations. Problem 78 focuses on determining the slope of a line using given points and understanding the concept of rise over run. Problem 79 deals with calculating the time it takes for one car to be a certain distance ahead of another, using concepts of relative speed and constant rates.

If Miss Smith's income in 1990 was $30,000, what would her income be in 1991 if it increased by 20%?

• $32,000

• $30,000

• $36,000

• $35,000

What was Miss Smith's total income for 1990 if she earned $17,500 in the first half and $20,000 in the second half?

• $40,000

• $35,000

• $37,500

• $30,000

Which of the following statements is sufficient to determine Miss Smith's income in 1991?

• Both statements are needed.

• Her income for the last six months of 1990 was $20,000.

• Her income for the first six months of 1990 was $17,500.

• Her income for 1991 was $7,500 more than 1990.

If Miss Smith's income for 1991 was $7,500 more than 1990, and her 1990 income was $37,500, what was her income in 1991?

• $45,000

• $42,000

• $43,000

• $44,000

In a coordinate plane, if the coordinates of point Q are (3, 4) and point P are (-2, -1), what is the slope of the line connecting these points?

• 1

• 2

• 0.5

• -1

What is the formula to calculate the slope of a line given two points (x1, y1) and (x2, y2)?

• (y2 - y1) / (x2 - x1)

• (x1 - x2) / (y1 - y2)

• (x2 - x1) / (y2 - y1)

• (y1 - y2) / (x1 - x2)

What is the change in y over change in x for a line with points (c, d) and (a, b)?

• d - b over c - a

• c - a over d - b

• a - c over b - d

• b - d over a - c

If car X is traveling at 50 mph and car Y at 40 mph, how long will it take for car X to be 2 miles ahead of car Y?

• 12 minutes

• 6 minutes

• 10 minutes

• 15 minutes

If car X was 1/2 mile ahead of car Y 3 minutes ago, how long will it take for car X to be 1 mile ahead?

• 6 minutes

• 3 minutes

• 12 minutes

• 9 minutes

If car X is 1 mile ahead of car Y, and both are traveling at constant speeds, how many minutes will it take for car X to be 2 miles ahead if car X travels 10 mph faster than car Y?

• 6 minutes

• 8 minutes

• 12 minutes

• 10 minutes