Question

increasing a by b percent yields 12 while decreasing a by b percent gives 8. what is the value of a and b

Answer 1

a + (b/100)a = 12
a( 1 + b/100) = 12

a - (b/100)a = 8
a( 1 - b/100) = 8

divide the top equation by the last one

(1+b/100)/( 1 - b/100) = 12/8 = 3/2
2 + 2b/100 = 3 - 3b/100
times 100
200 + 2b = 300 - 3b
5b = 100
b = 20

back in a(1-b/100) = 8
a(1 - 20/100) = 8
a(1 - 1/5) = 8
a(4/5) = 8
a = 40/4 = 10

a = 10, b = 20

check: if b=20% and a = 10
20% of 10 = 2
so adding 2 gives us 12
subtracting 2 gives us 8

my answer is correct