MHB Find Integer Part of A: Math Problem

[Albert1]

$A=(\dfrac{16\times72+17\times73+18\times74+19\times75}{16\times71+17\times72+18\times73+19\times74})\times 150$
find the integer part of A

 

[kaliprasad]

Spoiler

A = $( 1+\frac{16+ 17+ 18 + 19}{16 * 71 + 17 * 72 + 18 * 73 + 19 * 74}) * 150$
= $150 +\frac{16 * 150 + 17 * 150 + 18 * 150 + 19 *150}{16 * 71 + 17 * 72 + 18 * 73 + 19 * 74}$
= $150 + 2 +\frac{16 *8 + 17 * 6 + 18 * 4 + 19 *2}{16 * 71 + 17 * 72 + 18 * 73 + 19 * 74}$

so ans = 152

 

[Albert1]

Spoiler

A = $( 1+\frac{16+ 17+ 18 + 19}{16 * 71 + 17 * 72 + 18 * 73 + 19 * 74}) * 150$
= $150 +\frac{16 * 150 + 17 * 150 + 18 * 150 + 19 *150}{16 * 71 + 17 * 72 + 18 * 73 + 19 * 74}$
= $152 +\frac{16 * 8 + 17 * 6 + 18 * 4 + 19 *8}{16 * 71 + 17 * 72 + 18 * 73 + 19 * 74}$


so ans = 152

it should be:
= $152 +\frac{16 * 8 + 17 * 6 + 18 * 4 + 19 *2}{16 * 71 + 17 * 72 + 18 * 73 + 19 * 74}$indeed very smart solution:)