algebra problem

Question

Alex’s salary is z thousands of dollars per year, then he received a t% raise. Kyle’s salary

is t thousands of dollars per year, then he received a z% raise.

Compare the dollar amount of Alex and Kyle’s raises. Which one is larger and why, if

any? Are they equal and how would you know?

Answer 1

Alex's raise: (t/100)z → tz/100

Kyle's raise (z/100)t → zt/100

The raises are identica,

Answer 2

For example, let z = 20,000 dollars per year

Let t=25% then after Alex's raise he gets $25,000

25% = 1/4. 1/4 of 20,000 is 5,000

20,000+5,000= 25,000

Kyle made $25,000 and got a 20% raise

so now he makes $30,000. 20%=1/5

1/5 of $25,000 = $5,000

$25,000+$5,000 = $30,000

So Kyle is better off, but each got the same identical raise: $5,000

For Alex, initial income + raise = z+tz = z(1+t) = income after raise

For Kyle, initial income + raise t+tz= t(1+z) = income after raise

in both cases the raise = tz, so their raises are always equal

no matter what t and z are