 # Algebra: Substituting Numbers with Formulae

In this worksheet, students use algebra to solve numerical problems. Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Substitute Numerical Values for Formulae/Expressions

Difficulty level:   ### QUESTION 1 of 10

The main purpose of algebra is to solve problems.

But first, we must "translate" the problems into algebra.

The procedure for translation is generally as follows:

(a)   Let a letter stand for the quantity to be found in the question.  (e.g.  Let the missing number be x)

(b)   State the units of measurement if necessary.  (e.g.  Let the distance be x metres)

(c)   Write statements involving the missing quantity and form an equation to connect them.

(d)   Solve the equation algebraically.

(e)   Translate the answer back into English.   (e.g.  the distance is 2.5 km)

(f)    Check the numerical answer with the facts given in the original question.

Example

I think of a number and multiply it by 6.  After adding 20 to the result, my answer is 2.  What is the number I first thought of?

(a)    Let the number I first thought of be x.

(c)    When I multiply by 6 and add 20, this becomes 6x + 20.  This is equal to 2.

The equation is:

6x + 20 = 2

(d)    Solve to get:

6x = -18

x = -3

(e)    The number I first thought of is -3

(f)    -3 × 6 = -18

-18 + 20 = 2 so it works.

I think of a number and multiply it by 5.  After adding 20 to the result, my answer is 35.

Using x for the number I first thought of, select the equation which fits the given information.

5x - 20 + 35

5x + 20 = 35

20x + 5 = 35

I think of a number and multiply it by 5.  After adding 20 to the result, my answer is 35.  What is the number I first thought of?

Use algebra to form an equation, solve it and then state the number I first thought of.

A number is multiplied by 8 and then 11 is subtracted from the result.  The answer is 21.

Using x for the original number, select the equation which fits the given information.

11 - 8x = 21

8x = 21 - 11

8x - 11 = 21

A number is multiplied by 8 and then 11 is subtracted from the result.  The answer is 21.

Use algebra to form an equation, solve it and then state the original number.

Mark has a certain number of sweets.  He eats half of them and then gives 2 to his sister.  He has 2 left.

Using x for the number of sweets he had originally, select the equation which fits the given information.

2x - 2 = 2

½x + 2 = 2

½x - 2 = 2

Mark has a certain number of sweets.  He eats half of them and then gives 2 to his sister.  He has 2 left.

Use algebra to form an equation, solve it and then state the number of sweets which Mark had originally.

I think of a number and multiply it by 5.  After adding 10 to the result, my answer is -15.

Using x for the number I first thought of, select the equation which fits the given information.

5x + 10 = -15

5x + 10 = 15

10x + 5 = -15

I think of a number and multiply it by 5.  After adding 10 to the result, my answer is -15.

Use algebra to form an equation, solve it and then state the number I first thought of.

After a car journey, only a quarter of the petrol that I had at the start is left in the tank.  I stop at a petrol station and add 20 litres of petrol.  I now have a total of 31 litres in the tank.

Using x for the number of litres of petrol originally in the tank, select the equation which fits the given information.

¼x + 31 = 20

4x + 20 = 31

¼x + 20 = 31

After a car journey, only a quarter of the petrol that I had at the start is left in the tank.  I stop at a petrol station and add 20 litres of petrol.  I now have a total of 31 litres in the tank.

Use algebra to form an equation, solve it and then state the number of litres which were in the tank originally.

(just write the number)

• Question 1

I think of a number and multiply it by 5.  After adding 20 to the result, my answer is 35.

Using x for the number I first thought of, select the equation which fits the given information.

5x + 20 = 35
• Question 2

I think of a number and multiply it by 5.  After adding 20 to the result, my answer is 35.  What is the number I first thought of?

Use algebra to form an equation, solve it and then state the number I first thought of.

3
EDDIE SAYS
5x + 20 = 35
5x = 15
x = 3
• Question 3

A number is multiplied by 8 and then 11 is subtracted from the result.  The answer is 21.

Using x for the original number, select the equation which fits the given information.

8x - 11 = 21
• Question 4

A number is multiplied by 8 and then 11 is subtracted from the result.  The answer is 21.

Use algebra to form an equation, solve it and then state the original number.

4
EDDIE SAYS
8x - 11 = 21
8x = 32
x = 4
• Question 5

Mark has a certain number of sweets.  He eats half of them and then gives 2 to his sister.  He has 2 left.

Using x for the number of sweets he had originally, select the equation which fits the given information.

½x - 2 = 2
• Question 6

Mark has a certain number of sweets.  He eats half of them and then gives 2 to his sister.  He has 2 left.

Use algebra to form an equation, solve it and then state the number of sweets which Mark had originally.

8
EDDIE SAYS
½x - 2 = 2
½x = 4
½x × 2 = 4 × 2
x = 8
• Question 7

I think of a number and multiply it by 5.  After adding 10 to the result, my answer is -15.

Using x for the number I first thought of, select the equation which fits the given information.

5x + 10 = -15
• Question 8

I think of a number and multiply it by 5.  After adding 10 to the result, my answer is -15.

Use algebra to form an equation, solve it and then state the number I first thought of.

-5
EDDIE SAYS
5x + 10 = -15
5x = -25
x = -5
• Question 9

After a car journey, only a quarter of the petrol that I had at the start is left in the tank.  I stop at a petrol station and add 20 litres of petrol.  I now have a total of 31 litres in the tank.

Using x for the number of litres of petrol originally in the tank, select the equation which fits the given information.

¼x + 20 = 31
• Question 10

After a car journey, only a quarter of the petrol that I had at the start is left in the tank.  I stop at a petrol station and add 20 litres of petrol.  I now have a total of 31 litres in the tank.

Use algebra to form an equation, solve it and then state the number of litres which were in the tank originally.

(just write the number)

44
EDDIE SAYS
¼x + 20 = 31
¼x = 11
¼x × 4 = 11 × 4
x = 44
---- OR ----

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