Algebra with Whole Numbers

Algebra with Whole Numbers

Write equations and Solve

Write down the equation and solve it for n

• I think of a number, multiply it by 2 and then add 8. The answer is 50. Find the number.


• I think of a number, multiply it by 3 and then subtract 9. The answer is 60. Find the number.


• I think of a number, divide it by 2 and then add 6. The answer is 30. Find the number.


• I think of a number, divide it by 3 and then subtract 5. The answer is 20. Find the number.

Write down the equation and solve it for x

• John is 5 years older than Mary. Their ages total 33 years. Find their ages.

• (Let Mary’s age be x years.)










Mary is 14 and John is 19.


• James is 8 years younger than Margaret. Their ages total 42 years. Find their ages.

• (Let Margaret's age be x years.)










Margaret is 25 and James is 17.


• Dad is twice as old as Dave and together their ages total 63 years. Find their ages.

• (Let Dave's age be x years.)










Dave is 21 and his dad is 42.


• Steptoe is 3 times the age of his son and 46 years older than his son. Find their ages. (Let the son's age be x years).







The son is 23 and Steptoe is 69.


• Peter and Paul together earn a total of $500 every week. Of this Peter earns $40 more than Paul. Find how much each one earns per week.

• (Let Paul earn $x).

Paul earns is $230 and Peter earns $270.


• Mary and Jane together earn a total of $600 every week. Of this Mary earns $80 less than Jane. Find how much each one earns per week.

• (Let Jane earn $x).










Jane earns is $340 and Mary earns $260.


• Michael earns 3 times as much as Geoffrey and together their wages total $84 000 for the year. Find how much each one earns per annum.

• (Let Geoffrey earn $x).







Geoffrey earns is $21000 and Michael earns $63000.


• May earns 4 times as much as June and this amounts to a difference in their wages of $60 000 for the year. Find how much each one earns per annum.

• (Let June earn $x).







June earns is $20000 and May earns $80000.


• Tom is twice as old as Dick. Harriot is 3 times as old as Dick. Altogether their ages total 120 years. Find their ages.

• (Let Dick's age be x years).







Dick is 20, Tom is 40 and Harriot is 60.


• Peter is 7 years older than Paul. Mary is 3 years younger than Paul. Altogether their ages total 64 years. Find their ages.

• (Let Paul's age be x years).







Paul is 20, Peter is 27 and Mary is 17.


• Dad is twice as old as his son. His daughter is 5 years younger than his son. Altogether their ages total 95 years. Find their ages.

• (Let the son's age be x years).







The son is 25. Dad is 50 and the daughter is 20.


• Grandma is 3 times as old as Mum. Dad is 6 years older than Mum. Altogether their ages total 156 years. Find their ages.

• (Let the Mum's age be x years).







Mum is 30. Grandma is 90 and Dad is 36.


• Two angles are supplementary if they add up to . Find the 2 supplementary angles which are such that one is more than the other.

• (Let the smaller of the 2 angles be ).







One angle is 450 and the other is 1350.


• Two angles are complementary if they add up to 900. Find the 2 complementary angles which are such that one is 5 times the other. (Let the smaller of the 2 angles be x).





One angle is 150 and the other is 750.


• The angles of a triangle add up to 1800. Find the size of the angles in triangle ABC if angle B is 200 less than angle A and angle C is 3 times angle A.

• (Let the size of angle A be).







A = 400, B = 200 and C = 1200.


• The angles of a quadrilateral add up to 3600. Find the size of the angles in quadrilateral ABCD if angle B is 300 less than angle A, angle C is 400 more than angle A and angle D is twice angle A. (Let the size of angle A be x).


• The angles of a quadrilateral add up to 3600. Find the size of the angles in quadrilateral ABCD if angle B is 300 less than angle A, angle C is 400 more than angle A and angle D is twice angle A. (Let the size of angle A be x).

A = 700, B = 400, C = 1100 and D=140.

Exercise 13

1. The distance, d km, that an athlete walks is given by the formula where t is the time

for which she walks in hours.

• Find the distance she walks in 3 hours.

• Find the time it takes her to walk the length of a marathon (i.e. 42 km).

2. The distance, d km, that an athlete jogs is given by the formula where t is the time

for which he jogs in minutes.

• Find the distance that he jogs in 1 hour (i.e. 60 minutes).

• Find the time (in hours and minutes) for him to jog the length of a half marathon (i.e. 21 km).

3. The money saved by a youth since her 12th birthday, $S, is given by the formula where n is the

number of weeks which have elapsed since her 12th birthday.

Find how much she saved

• by her next birthday (i.e. 52 weeks after her 12th birthday).

• initially (i.e. on her 12th birthday).

3. The money saved by a youth since her 12th birthday, $S, is given by the formula where n is the

number of weeks which have elapsed since her 12th birthday.

• Find how many weeks after her 12th birthday she will have saved $1000

4. The temperature, t, of water in a kettle is given by the formula where n is the number of seconds after

the kettle was turned on. Find the temperature of the

water in the kettle

• 200 seconds after it was turned on

• 2 minutes (i.e. 120 seconds) after it was turned on

• initially (i.e. at the instant that the kettle was turned on).


the kettle was turned on. Find (in minutes and

seconds) how long it takes for the water in the kettle

• to reach body temperature (i.e. 370 C.)

• to boil (i.e. to reach 1000 C.)


the kettle was turned on. Find (in minutes and

seconds) how long it takes for the water in the kettle

• to reach body temperature (i.e. 370 C.)

• to boil (i.e. to reach 1000 C.)

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Algebra with Whole Numbers