Direct Proportion

A is directly proportional to B.

When A = 12, B = 3.

Find a formula for A in terms of B.

• B = 4A

• 
  

  $B\ =\ \frac{A}{4}$

• A = 4B

• $A\ =\ \frac{B}{4}$

Answer explanation

A = k x B

12 = k x 3

K = 12 $\div$ 3 = 4


So, A = 4 x B
A = 4B

A is directly proportional to B.

When A = 12, B = 3.

Find A when B = 5.

(a)  

A is directly proportional to B.

When A = 12, B = 3.

Find B when A = 36.

(a)  

C is directly proportional to D.

When C = 125, D = 5.

Find a formula for C in terms of D.

• C = 25D

• 
  

   $C\ =\ \frac{D}{25}$ 

• D = 25C

•  $D\ =\ \frac{C}{25}$ 

Answer explanation

C = k x D

125 = k x 5

K = 125  $\div$ 5 = 25


So, C = 25 x D
C = 25D

C is directly proportional to D.

When C = 125, D = 5.

Find C when D = 10.

(a)  

C is directly proportional to D.

When C = 125, D = 5.

Find D when C = 75.

(a)  

E is directly proportional to F.

When E = 2, F = 8.

Find a formula for E in terms of F.

• E = 4F

• E=0.25F

• F=4E

• F=0.25E

Answer explanation

E = k x F

2 = k x 8

K = 2  $\div$ 8 = 0.25


So, E = 0.25 x F
E = 0.25F

E is directly proportional to F.

When E = 2, F = 8.

Find E when F = 30.

(a)  

E is directly proportional to F.

When E = 2, F = 8.

Find F when E = 100.

(a)  

Y is directly proportional to X.

When X = 400, Y = 10.

Find a formula for Y in terms of X.

• Y = 40X

• Y=0.025X

• X=40Y

• X=0.025Y

Answer explanation

Y = k x X

10 = k x 400

K = 10  $\div$ 400 = 0.025


So, Y = 0.025 x X
Y = 0.025X

You have to be extra careful here.  The informaion in the question is not in quite the same order as in the previous questions.