PROJECT IN MATHEMATICS

WORD PROBLEMS IN ALGEBRA

Bernardine InocencioOctober 3, 2009

PROBLEM 1 - AGE PROLEM

• John’s father is 5 times older than John and John is twice as old as his sister Alice. In two years time, the sum of their ages will be 58. How old is John now?

PROBLEM 1 - REPRESENTATION

• Let x be John’s age now. Add 2 to get the ages in 2 yrs.

PROBLEM 1 - WORKING EQUATION

• In two years time, the sum of their ages will be 58.

PROBLEM 1 - SOLUTION

PROBLEM 1 - CONCLUSION

• John is now 8 years old.

PROBLEM 2 - DIGIT PROBLEM

• The ten’s digit of a number is three times the one’s digit. The sum of the digits in the number is 8. What is the number?

PROBLEM 2 - REPRESENTATION

• Let x = one’s digit3x = ten’s digit

PROBLEM 2 - WORKING EQUATION

• The sum of the digits in the number is 8.

x + 3x = 8

PROBLEM 2 - SOLUTION

x + 3x = 84x = 8x = 2

• The one’s digit is 2. The ten’s digit is 3 × 2 = 6

PROBLEM 2 - CONCLUSION

• The number is 62.

PROBLEM 3 - DISTANCE PROBLEM

• A bus and a car leave the same place and traveled in opposite directions. If the bus is traveling at 50 mph and the car is traveling at 55 mph, in how many hours will they be 210 miles apart?

PROBLEM 3 - REPRESENTATION

• Let t = time when they are 210 miles apart. • Fill in the values for d using the formula d = rt

PROBLEM 3 - WORKING EQUATION

• Since the total distance is 210, we get the equation:

50t + 55t = 210

PROBLEM 3 - SOLUTION

50t + 55t = 210105t = 210

t = 210/105 = 2

PROBLEM 3 - CONCLUSION

• They will be 210 miles apart in 2 hours.

PROBLEM 4 - INTEGER PROBLEM

• The sum of the least and greatest of 3 consecutive integers is 60. What are the values of the 3 integers?

PROBLEM 4 - REPRESENTATION

• Let x = least integerx + 1 = middle integerx + 2 = greatest integer

PROBLEM 4 - WORKING EQUATION

• The sum of the least and greatest is 60.

x + (x + 2) = 60

PROBLEM 4 - SOLUTION

x + (x + 2) = 60 2x + 2 = 60

2x =58x = 58/2 = 29

• The least integer is 29. The middle integer (x+1) is 30. The greatest integer (x+2) is 31.

PROBLEM 4 - CONCLUSION

• The 3 consecutive numbers are 29, 30 and 31.

THANK YOU !