SOLUTION: the salary of A is 20% below the salary of B and the salary of C is 56.25% greater than the salary of A. by how much % is the salary of B less than the salary of C.

Question 965470: the salary of A is 20% below the salary of B and the salary of C is 56.25% greater than the salary of A.

by how much % is the salary of B less than the salary of C.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the salary of A is 20% below the salary of B and the salary of C is 56.25% greater than the salary of A.

by how much % is the salary of B less than the salary of C?

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salary of A is .8 * B.

this is because 20% less than salary of B is equal to B - .20 * B which is equal to (1 - .2) * B which is equal to .8 * B.

salary of C is 1.5625 * salary of A.

this is because 56.25% greater than A is equal to A + .5625 * A which is equal to (1 + .5625) * A which is equal to 1.5625 * A.

so you have:

A = .8 * B
C = 1.5625 * A.

in the equation of A = .8 * B, solve for B to get B = A / .8 which is the same as 1/.8 * A which simplifies to B = 1.25 * A.

you now have:

A = .8 * B
B = 1.25 * A
C = 1.5625 * A.

you want to know what percent the salary of B is less than C.

the formula for this would be:

(C - B) / C * 100%

since B = 1.25 * A and C = 1.5625 * A, this formula becomes:

(C - B) / C * 100% = [(1.5625 * A - 1.25 * A) / (1.5625 * A)] * 100%

The A in the denominator and the A in the numerator cancel out and you are left with:

(C - B) / C * 100% = [(1.5625 - 1.25) / 1.5625] * 100%.

sinplify this to get (C - B) / C * 100% = 20%.

that's your solution.

B is 20% less than C.

to see if you're correct, give some values to A and B and C and see if this makes sense.

let B = 1000
this means that A is equal to 800 because A is equal to 80% of B.
this means that C is equal to 1250 because 80% of 1250 is equal to 1000.

if the numbers are correct, than C must be 56.25% greater than A.

800 * 1.5625 is equal to 1250.

the numbers check out so the solution appears to be good.

i'd go with it.

solution is that B is 20% less than C.

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