Algebra question

Question

A + (20% of A) = B
B + (20% of B) = C
A + (X% of A) = C

What number is X?

Answer 1

By substitution, you can find the following:

 

A + 0.2 A = 1.2A = B

 

B + 0.2 B = 1.2B = C 

1.2B = 1.2*(1.2A) = 1.44A = C

 

 

Since 1.44A = C, you must add 0.44 to A to get C.

 

0.44 is 44% so X is 44.

Answer 2

A + (20% of A) = B or 1.2A = B
B + (20% of B) = C or 1.2B = C

 

Replace B in the second equation with 1.2A

 

1.2(1.2A) = C

1.44A = C or A + .44A = C

 

Therefore X = 44%

 

 

Answer 3

A + 0.20A = B

B + 0.20B = C

A + xA     = C

 

In the last equation, you can substitute in for C.

A +  xA = B + 0.20 B

 

now substitute for B

A + xA = A + 0.20 A + 0.20(A + 0.20 A)

 

now distribute and then combine like terms

 A + xA = A + 0.20 A + 0.20 A + 0.04 A

-A           -A

xA = 0.44 A

(xA)/A = (0.44 A)/A

x = 0.44

 

or x = 44 %