Solved Math Problems

Various types solved math problems are given below.

1. Kris is 2 meters tall and casts a shadow of 4 meters long. At the same time, a tree casts a shadow 10 meters long. How tall is the tree? The tree is____ m.

Answer: 5 m

2. The ratio of boys to girls in Art class is 1 : 2. There are 12 girls in the class. How many boys are there?

Answer: 6 boys.

3. A hiker is on a trail going up a hill. If he ascends 4 vertical feet for every 10 feet he walks forward, what is his rate of change? Express the vertical change to the horizontal change as a ratio.

a. \(10\over 4 \) b. \(2\over 5 \) c. \(1\over 2 \) d. \(5\over 2 \)

Answer: b. \(2\over 5 \)

4. What is the Standard Form of a linear equation?

a. \(m = \frac{y_2-y_1}{x_2-x_1}\)

b. y = mx + b

c. \(y - y_{1} = m(x - x_{1})\)

d. Ax + By = C

Answer: d. Ax + By = C

5. What is the Slope-Intercept Form of a linear equation?

a. \(y - y_{1} = m(x - x_{1})\)

b. Ax + By = C

c. \(m = \frac{y_2-y_1}{x_2-x_1}\)

d. y = mx + b

Answer: d. y = mx + b

6.  What is the Point-Slope Form of a linear equation?

a. \(y - y_{1} = m(x - x_{1})\)

b. \(m = \frac{y_2-y_1}{x_2-x_1}\)

c. Ax + By = C

d. y = mx + b

Answer: a. \(y - y_{1} = m(x - x_{1})\)

7. What is the slope formula?

a. Ax + By = C

b. \(m = \frac{y_2-y_1}{x_2-x_1}\)

c. y = mx + b

d. \(y - y_{1} = m(x - x_{1})\)

Answer: b. \(m = \frac{y_2-y_1}{x_2-x_1}\)

8. Write an equation in slope-intercept form of the line that goes through the points (2, 3) and (0, 0) y = ___ x + ___

Answer: y = \(3\over2 \) x + 0

9. Write an equation in slope-intercept form of the line that has a slope of -2 and a y-intercept of 9. y = ___ x + ___

Answer: y = - 2x + 9

10. Write an equation in point-slope form of the line that has a slope of \(1\over3 \) and goes through the point (3, 7) y - ___ = ___ (x - ___)

Answer: y  - 7 = \(1\over3 \) (x - 3 )

11. What is the slope of this line? 2x + y = 4

Answer: Slope = -2

12. The equation of a line of best fit relating the money earned at a bake sale to the number of customers is e = 0.9c + 18. Predict the earnings for a bake sale that has 90 customers.

Answer: 99

13. In a class of 50 students, 40% are girls. only girls are added to the class until the percent of the girls increases to 60%. How many girls were added to the class?

Answer: 25

14. Jennifer wants to buy a new outfit. She has a choice between 4 pairs of pants, 2 blouses, and 3 pairs of shoes. How many different outfits can she make consisting of 1 pair of pants, 1 blouse, and 1 pair of shoes?

Answer: 24

15. Sunny is looking at different types of suncreen. There are 3 different types of sunscreen with SPF 45, 5 types of sunscreen with moisturizer, and 6 different types of sunscreen with spf 15. In how many different ways can sunscreen be bought?

Answer: 90

16. A race with 18 people is going to take place in central park. How many different way can there be a first, second, and thrid plae winner?

Answer: 4896

17. If Brabara ran a mile in 5 minutes, 6 minutes, and 8 minutes, how much time would she need on her fourth run to average 7 minutes?

Answer: 9 minutes

18. While driving new car for six months Tommy drives 300 miles in first month at a cost of $296. then second month 225 mi at cost of $279.50. Assuming related in linear function what would be linear equation relating?

19. If a varies inversely as the square of b, and a is 9/49 when b is 7, find a when b is 5.

Solution:

a varies inversely as the square of b

a ∝ \(\frac{1}{b^2}\)

a = k ∙ \(\frac{1}{b^2}\)

a is \(\frac{9}{49}\) when b is 7

\(\frac{9}{49}\) = k ∙ \(\frac{1}{7^2}\)

\(\frac{9}{49}\) = k ∙ \(\frac{1}{49}\)

k = 9

Therefore, a =  \(\frac{9}{b^2}\)

Now b = 5

Then,

a = \(\frac{9}{5^2}\)

a = \(\frac{9}{25}\)

Answer: \(\frac{9}{25}\)

20. If 5 out of 25 people like chocolate ice cream, what percent of the people do NOT like chocolate ice cream?

Answer: 80%

21. You buy a $500 certificate of deposit and the end of two years you cash it in for $583.20. What is the annual yield on this investment? Round to one decimal place.

22. Two factories blow their whistles at exactly the same time. If a man hears the two blasts exactly 2.3 seconds and 6.7 seconds after they are blown and the angle between his lines of sight to the two factories is 46.4°, how far apart are the factories? Give your result to the nearest meter. (Use the fact that sound travels at 344 m/sec)

23. If x people can do a job in d days, how long would it take y people to do the same job?

24. A group of Boy Scouts on a straight trail headed N30.6E found the trail led through a briar patch. They chose to walk 156meters due east along the south edge of the briar patch then due north along the east edge of the patch back to the trial. How much farther did they walk to avoid walking through the briar patch?

25. Translate from English to algebra: Mr Smithson gets 15 mL per day of dextrose 5% in water. Mr. Smithson should receive 5 mL less than Mr. Hamir per day. Use x for the amount Mr. Hamir gets.

A) 5 - x = 15  B) 5 + x = 15  C) x - 5 = 15  D) 5x = 15  E) 15 - x = 5  F) x - 15 = 5

Answer: C) x - 5 = 15

26. A multi-use 100 mL vial of bacteriologist water has had x number of 4 mL doses drawn from it. There are 52 mL left. How many doses were drawn?

Answer: 12

27. You have drawn x units of insulin into a 100 unit syringe. You need to have 30 units total. Write an expression for how many more units you must draw.

A) 100+x B) 30-x C) 100-x D) 100+x E) 30+x F) x-30 G) x-100

Answer: B) 30-x

28. Dan owns a vacant lot that is 32m wide and 40m long. He makes a rectangular basketball court in the middle by subtracting equal amounts of the length and width. The area of the court is 560 m^2. How far from the edge of the lot is an edge of the court

29. In a particular country, railroad miles have been on the decline and the miles of roads in the highway system have been increasing. The function y = -1378.6x + 134,454 represents the railroad miles,where the function y = 466.3x + 154,226 models the number of highway miles. For each function, x is the number of years after 1995.

30. Suppose that 6% of the seniors and 3% of the juniors at new iberia senior high scorea a 27 or greater on their ACT. There are 5 times as many seniors as juniors at t the school. what percentage of the seniros and juniors taken together scored greater than a 27 on the ACT? Express your answer to the nearest tenth.

31. Tina lives 350 m from school. She walks to school and home again each day. During a 5 day school week, how far does she walk?

A. 3.5 km B. 1.75 km C. 70 km D. 1,750 km

Answer:  A. 3.5 km

32. Jim Finley is a professional photographer. He has a photo 8 cm long and 6 cm wide. A customer wants a print of the photo. The print is to have half the area of the original. Jim plans to reduce the length and width of the photo by the same amount. what are the dimensions of the pring?

Answer: Hint: (8 - x)( 6 - x) = \(1\over2 \)(8 × 6)

             Length = 6 cm wide = 4 cm.

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