Question 159384
thirteen years ago, Mary's age was 5/17 of Grace's age. Two years from now Mary will be 1/2 of Jim's age. Together all their ages add up to 118. Find their ages five years from now.
:
Let m = Mary's age now
Let g = Grace's age now
:
Write an equation/expression for each statement
:
"thirteen years ago": that would be:
(m-13) and (g-13)
:
" Mary's age was 5/17 of Grace's age."
m - 13 = {{{5/17}}}(g-13)
Multiply equation by 17 to get rid of that annoying denominator, results:
17(m-13) = 5(g-13)
17m - 221 = 5g - 65
or
5g - 65 = 17m - 221
5g = 17m - 221 + 65
5g = 17m - 156
g = {{{((17m-156))/5}}}
;
" Two years from now Mary will be 1/2 of Jim's age."
Where did Jim come from? Anyway: j = jim's age now:
:
(m+2) = .5(j+2)
or
j + 2 = 2(m+2)
j = (2m+4) - 2
j = 2m + 2

:
 Together all their ages add up to 118.
m + g + j = 118
: 
Substitute for g and j
m + {{{((17m-156))/5}}} + (2m+2) = 118
Multiply equation by 5, results:
5m + (17m-156) + 5(2m+2) = 5(118)
5m + 17m - 156 + 10m + 10 = 590
32m - 146 = 590
32m = 590 + 146
32m = 736
m = {{{736/32}}}
m = 23 yrs is Mary's present age
then
j = 2(23)+ 2)
j = 46 + 2
j = 48 yrs is Jim's present age
and
g = {{{((17(23)-156))/5}}}
g = {{{((391-156))/5}}}
g = {{{235/5}}}
g = 47 yrs is Grace's present age
:
Check 23 + 48 + 47 = 118
:
 Find their ages five years from now. Just add 5 to the above ages:
Mary 28, Grace 52, Jim 53