Question 11 a,b,c GCSE 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!!!

Question 11 a,b,c GCSE question ??
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)
Reply: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)
Reply: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)
Reply: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)