Question 149108
Let {{{B}}} = Bob's age now
Let {{{T}}} = Tom's age now
{{{B = (1/2)*T}}}
{{{B - 1}}} = Bob's age 1 year ago
{{{T + 1}}} = Tom's age 1 year from now
{{{B - 1 = (2/5)*(T + 1)}}}
{{{5*(B - 1) = 2*(T + 1)}}}
{{{5B - 5 = 2T + 2}}}
{{{5B = 2T + 7}}}
Since
{{{B = (1/2)*T}}}
{{{(5/2)*T = 2T + 7}}}
{{{5T = 4T + 14}}}
{{{T = 14}}}
{{{B = (1/2)*14}}}
{{{B = 7}}}
Bob's age is 7 and Tom's age is 14
check:
{{{B - 1 = (2/5)*(T + 1)}}}
{{{7 - 1 = (2/5)*(14 + 1)}}}
{{{6 = (2/5)*15}}}
{{{30 = 30}}}
OK