Question

If a is 10% greater than b, and ac is 32% greater than bd, then c is what percent greater than d?

Answer 1

"a is 10% greater than b" in math language is:
\[a = 1.10b\]
"ac is 32% greater than bd" in math language is:
\[ac = 1.32bd\]
Using substitution:
\[ac = 1.32bd \Rightarrow 1.10bc = 1.32bd \Rightarrow 1.10c = 1.32d \Rightarrow c = 1.20d\]
Which in english means that c is 20% greater than d.

Answer 2

Oh ok but how do you convert to math language?

Answer 3

if a is 10% greater than b, that means you took b, multiplied it by .10, and then added it to itself:
\[b(.10)+b = b(.10+1) = 1.10b\]

Answer 4

ooh i get it now. thank you :D