A/B = 5/2
=> 2A = 5B
=> 8A = 20B

8A+9B:8A+2B = (8A+9B)/(8A+2B)
= (20B+9B)/(20B+2B)
= 29/22

IMO D

pzazz12 wrote:If A:B = 5:2 the value of 8A+9B:8A+2B is

A) 26:16
B) 61:26
C) 22:29
D) 29:22
E) 26:22

Take A as 5 and B as 2

Now substitute it in 8A+9B:8A+2B

8*5+9*2 = 58 No need to go any further , check the options and you can find option D which is a factor of 58.

29*2 = 58.

So we can conclude D as the answer.

You can go further and check out 8A+2B

8*5+2*2 = 40+4 = 44

Thus the ratio 8A+9B:8A+2B comes to 58 / 44 = 29/22.


Here I have taken A as 5 and B as 2 because the final ratio is in the same power(indices) 8A+9B:8A+2B

Had it been 8A^2 + 9B^3 : 8A^3 + 2B^4 then this method would not be applicable.

Whenever I see proportions in the "A:B" format I suggest my students to think about the "k technique", that is, call A = 5k and B = 2k (where k is a non-null real constant).

Now you just substitute A and B in the expression asked... easy and quick!

Regards,
Fabio.

P.S.: when only a ratio is involved (I mean, something like "A:B"), I agree that the "k technique" is not a big deal... but things start to be nice when double (or more) ratios are concerned (I mean: "A:B:C" etc)... remember this and use is whenever possible!