Question 1120664
<br>
Their ages 20 years ago were in the ratio 9:11.  So let their ages then be 9x and 11x.<br>
It is a typical way to start work on a problem where a ratio is given.<br>
Then their current ages are 9x+20 and 11x+20; and those ages are in the ratio 7:8.  So<br>
{{{(9x+20)/(11x+20) = 7/8}}}
{{{77x+140 = 72x+160}}}
{{{5x = 20}}}
{{{x = 4}}}<br>
Their ages 20 years ago were 9x=36 and 11x=44; their ages now are 36+20=56 and 44+20=64.<br>
Answer: The older brother is now 64.<br>
You should know how to solve a problem like this using formal algebra; however, I always like to encourage students to try to solve a problem informally using logical reasoning -- it's good brain exercise.<br>
In this problem, we know their ages 20 years ago were in the ratio 9:11; that means the older brother's age was a multiple of 11.<br>
And we know that now the ratio of their ages is 7:8, so the older brother's age now is a multiple of 8.<br>
So we only need to find a multiple of 11 which increased by 20 is a multiple of 8.<br>
11+20 = 31  nope...
22+20 = 42  nope...
33+20 = 53  nope...
44+20 = 64  yep!!<br>
The older brother is now 64.