Question 1196797
This year, alex's grandfather's age is 6 times of Alex's age. After a few years, Alex's grandfather's age will be 5 times of Alex's age. After another few years, Alex's grandfather's age will be 4 times of Alex's age. What is Alex's grandfather's age this year?
<pre>Let grandfather’s age be G
Then Alex’ is {{{G/6}}}
Let “a few years” be y. Then: {{{matrix(5,3, 5(G/6 + y), "=", G + y, 5G/6 + 5y, "=", G + y, 4y, "=", G - 5G/6, 24y, "=", 6G - 5G, 24y, "=", G)}}}    Let “another few years,” or years after this year, be z. Then: {{{matrix(5,3, 4(G/6 + z), "=", G + z, 2G/3 + 4z, "=", G + z, 3z, "=", G - 2G/3, 9z, "=", 3G  -  2G, 9z, "=", G)}}}
                                                                    We then get: {{{matrix(3,3, 24y, "=", 9z, 24y/9, "=", z, 8y/3, "=", z)}}}

                     With {{{matrix(1,3, z, "=", 8y/3)}}}, ONLY MULTIPLES of 3 can be substituted for y in order to get INTEGER-VALUES for z

Therefore, if y = 3, then {{{matrix(1,5, z, "=", 8(3)/3, "=", 8)}}}
This gives us: G, or the <font size  = 4><font color = red><b>grandfather’s age</font></font></b> as: 24(3), or 9(8) = <font size  = 4><font color = red><b>72</font></font></b>.

With ONLY MULTIPLES of 3 that can be substituted for y, we substitute 6 for y to get: {{{matrix(1,5, z, "=", 8(6)/3, "=", 16)}}}
This gives us: G, or the grandfather’s age as: 24(6), or 9(16) = 144

As it’s HIGHLY UNLIKELY that the grandfather is 144 years old, no LARGER multiples of 3 need to be tried/substituted. 

Therefore, the more REALISTIC age for him is as stated above, 72.</pre>