Question 11 a,b,c GCSE question ??

Question

Fraction, p, of an adults dose of medicine which should be given toa child who weighs w kg is given by the formula p = (3w+20)/200

a) USe the formula to find weight of a child whose dose is the same as an adults dose.

b) Make w the subject of the formula p = (3w+20)/200

c) (3w+20)/200 = A/(A+12)
Express A in terms of w

Thanks to anyone who can answer this question, it would be really helpful!!!

Answer 1

a) p = (3w+20)/200
1 = (3w+20)/200 --- as p is 1 whole
200 = 3w+20
200-20 = 3w
180 = 3w
w = 60kg

b) p = (3w+20)/200
200p = 3w+20
200p-20 = 3w
w = (200p-20)/3
w = (20/3)(10p-1)

c) (3w+20)/200 = A/(A+12)
(3w+20)(A+12) = 200A
(3w+20)A + (3w+20)(12) = 200A
(3w+20)(12) = 200A - (3w+20)A
12(3w+20) = A(200-3w-20)
A = 12(3w+20) / (180-3w)
A = 12(3w+20) / 3(60-w)
A = 4(3w+20) / (60-w)

Answer 2

a) That would mean finding the weight w such that p = 1.
1 = (3w+20)/200
200 = 3w + 20
180 = 3w
w= 60 pounds is the weight of the child who gets an adult dose.

b) If p = (3w+20)/200
200p = 3w + 20
200p - 20 = 3w
w = (200p-20)/3

c) (3w+20)/200 = A/(A+12)
(A+12)*(3w+20)/200 = A
A* ( (3w+20)/200 - 1 ) = -12*(3w+20)/200
A = -12*((3w+20)/200) / ( (3w+20)/200 - 1 )
A = -12*(3w+20) / (3w+20-200)
A = -12*(3w+20) / (3w-180)
A = -4*(3w+20) / (w-60)

Answer 3

a. For an adult dose, p=1 (p is the fraction of an adult dose). So we set 1=(3w+20)/200, or 200=3w+20, or 3w=180, and w=180/3=60.

b. If p=(3w+20)/200 then 200p=3w+20, 200p-20=3w, and w=(200p-20)/3

c. If (3w+20)/200 = A/(A+12), then (3w+20)(A+12)=200A.
Using foil, we get 3wA+20A+36w+240=200A.
Put all of the stuff with A on one side to get
36w+240=200A-3wA-20A
or 36w+240=A(200-3w-20)
Now divide to get A=(36w+240)/(200-3w-20)

Answer 4

b)
p = (3w+20)/200
200p=3w+20
200p-20=3w

w=(200p-20)/3

c)
(3w+20)/200 = A/(A+12)
A=(12w+80)/(-w+60)