Question

If 1 x 10^a + 2 x 10^b + 3 x 10^c + 4 x 10^d = 24130 and a≠b≠c≠d, then what does a/2 + b/4 + c/8 + d/16 equal?

Answer 1

Question 1

Using scientific notation, we know a=2, b=4, c=1, and d=3. So,

`(a)/(2)+(b)/(4)+(c)/(8)+(d)/(16)=1+1+(1)/(8)+(3)/(16)=37/16`

Question 2

`a+13b=3(3a-b)\\\\a+13b=9a-3b\\\\16b=8a\\\\a=2b\\\\\therefore (a^3)/(b^3)=((2b)^3)/(b^3)=(8b^3)/(b^3)=8`