Question

9.

a 4p + 6q= 8
Write down the value of 8p + 12q

b) 20q - 5r = 45
Write down the value of 4q -r
(1 mark)
c)
Answer
(1 mark)
Use your answers to parts a) and b) to write an expression using p.q and r with
value of 41
Give your answer in its simplest form.​

Answer 1

Explanation:

4p + 6q = 8 ....multiply by 2

8p + 12q = 16 <==

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20q - 5r = 45 ....divide by 5

4q - r = 9 <===

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not sure I understand this one....

can it be something as simple as :

(8p + 12q) + (4q - r) + 16 ....because this equals 41

16 + 9 + 16

Answer 2

a) 16

b) 9

c) 16p +28q -r

Explanation:

a) The desired coefficients are double those given, so we can multiply the given equation by 2 to get ...

2(4p +6q) = 2(8)

8p +12q = 16 . . . . the desired value

__

b) The desired coefficients are 1/5 of those given, so we can divide the given equation by 5 to get ...

(20q -5r)/5 = 45/5

4q -r = 9 . . . . the desired value

__

c) There are an infinite number of ways the values 16 and 9 can be combined to get 41. One of the simplest is ...

2×16 + 9 = 41

Substituting the expressions of part (a) and (b), we get ...

2×(8p +12q) +(4q -r) = 41

16p +28q -r = 41