GRADE 7 MATH (SPECIAL CLASS)

Grade 7 Special Class

Review of Various Problem Solving Techniques

Write your answers and complete solutions on any sheet of paper, to be submitted upon the resumption of classes. Also, please download the pdf file found in the attached link http://www.mathdb.org/basic_calculus/BasicCalculus.pdf ; read Chapters 0, 1 and 2, and answer the exercises found in every section. Answers can be found in pages 255 onward for your reference. Please, PLEASE, master the different subsets of real numbers and the nature of each. Should you have any questions, feel free to email me at sigridgayangos@gmail.com or message me on Facebook. Enjoy solving!

Ratio and Proportion

1) A menu which serves 4 people requires 3 cups of flour. How many cups of flour are needed for the menu to serve 12 people?

2) To finish a certain job in 8 days, 6 workers are needed. If it is required to finish the same job in 2 days advance, how many workers would have to work?

3) A supply of food lasts for a week for 25 families. How long would the supply last if 5 more families have to be supplied?

4) Five people can finish painting a wall within 5 hours. If only 3 people are available, how many hours do they have to work to finish the same job?

Percentage Problems

5) Kristine has P 15 000 in the bank. After a year, she expects it to earn P 750. What is the rate of interest?

6) Jonathan invested P 3 500 in a buy and sell. How much will his money be in 2 years if it earns 15% interest a year?

7) Ellie saved P 150 from an item that would have cost her P 1 875. What was the percentage discount given her?

8) For every newspaper that he sells, a newspaper boy gets 25% commission. How many newspapers costing    P 7 each should he be able to sell if he wants to earn at least P90 for one day?

9) A salesman has a basic salary of P 20 000 and gets a commission of 8% on all sales above P 150 000. What will his total earnings be if his sales reach up to P 205, 000?

Evaluating Expressions Given Certain Conditions

10) x²-2xy; x=1/2 and y=1/3                           

11) (5x²-5y²)/(6y²-6x²); x=1/5 and y=1/3

Problem Solving in One or Two Variable(s)

12) The sum of the digits of a two-digit number is 14. The value of the number is two less than 11 times the tens digit. What is the number?

13) The digits of a positive two-digit number are reversed, resulting in a new number. It turns out that the sum of the two numbers is 11 times their difference. What are the two numbers if the sum of the digit is 9?

14) Eunice is three years older than Steve. When they got married 40 years ago, the difference of twice Eunice’s age from Steve’s age was 16. How old will each be when they celebrate their golden anniversary (50^th year)?

15) Marc’s present age is 2/3 that of Raimund. In 8 years, Marc’ age will be 4/5 that of Raimund’s. How old are they now?

16) Jason is twice as old as Joel while John is 6 years younger than Jason. If Joel’s age four years ago, Jason’s age now, and John’s age four years hence are summed up, the result is 34. What are their present ages?

17) A machine can print 40 booklets in an hour while a slower machine could only print 30 in an hour. If the two machines are utilized together, how long would it take both machines to print 840 booklets?

18) It takes one drainage pipe 3 hours to empty a pool of water. On the other hand, it takes a certain brand of inlet pipes 12 hours for each of them to fill an empty pool with water. How many of these inlet pipes are needed, so that when these pipes are left open with the drainage pipe, it will take 1 hour for the pool to be filled?

19) A jet goes against a headwind of 50kph for two and one-half hours, and returns the same distance assisted by the tailwind also in 50kph for 2 hours. What is the speed of the plane in still air?

20) A candy factory produces two kinds of candies. Lemon candies cost P28 per kilogram while strawberry candies cost P16 per kilogram. How much of each must the factory use to make a 42-kg mixture to sell at P20 per kilogram?

21) How much water must be distilled from 200L of an 8% alcohol solution to produce a 12% alcohol solution?

22) A 10L container is filled with juice that is 15% pure orange. How much of  this must be taken out and replaced with pure orange juice to increase the concentration to 30% pure orange juice?

23) P 12 000 is invested in a bank: part of it at 4% while the rest at 3%. How much is invested at each rate if the annual income from both investments is P450?

24) If one side of a square is doubled and the other side increased by 7 units, the resulting rectangle will have an area of 120 sq units. What is the length of a side of a square?

25) The area of a right triangle is 6 sq cm. Find its dimensions if its perimeter is twice its area.

26) Koko, Kevin and Karlo were given a set of assignments by their teacher. Working alone, Koko can finish the set in 30 minutes, Kevin in an hour, while Karlo in 75 minutes. Karlo started working at 5 pm. Kevin joined him after 10 minutes, and Koko joined them at 5.25 pm. How long did Kevin work?

27) The sum of the digits o a three-digit number is 15. If the tens and units digits are interchanged, the original number will be 9 more than the new number. If the units and the hundreds digits are interchanged, the new number will be 99 more than the original number. What is the original number?

28) A scientist wants to mix three solutions, A, B and C, to make a 165 ml solution that is 1/3 salt. The concentrations of the solutions are 50%, 33 1/3% and 20% respectively. What is the volume of each solution?

29) A delivery truck travels a distance of 200 km at a uniform rate. On a certain day, after travelling for 1 ½ hours, the truck broke down and it took the driver 30 minutes to fix it. However, the aped of the truck slowed down to ¾ of the original. Thus, it arrived 80 minutes later than usual. If the truck’s speed was 10kph greater than the original and there was no delay, the truck would have arrived 40 minutes earlier. What is the speed of the truck?

30) A plane can travel 600 miles with the wind and 900 miles against the wind in 3 3/10 hours. It can also travel 650 miles against a headwind and return in 2.925 hours. What is the speed of the plane in still air?