Question 542689
Let m = man's present age
Let d = daughter's
Let s = son's
:
Write an equation for each statement, simplify:
:
twelve years ago, a man was three times as old as his daughter.
m - 12 = 3(d - 12)
m - 12 = 3d - 36
m = 3d - 36 + 12
m = 3d - 24
:
" nine years from now, the man will be twice as old as his son."
m + 9 = 2(s + 9)
m + 9 = 2s + 18
m = 2s + 18 - 9
m = 2s + 9
:
"four years from now, the sum of the ages of the son and daughter will equal the age of the man."
m + 4 = s+4 + d+4
m + 4 = s + d + 8
m = s + d + 8 - 4
m = s + d + 4
replace m with (3d-24)
3d - 24 = s + d + 4
3d - d - s = 4 + 24
2d - s = 28
then in the same equation
m = s + d + 4
replace m with (2s + 9)
2s + 9 = s + d + 4
2s = s + d + 4 - 9
-d + 2s - s = - 5
-d + s = -5
:
Use elimination on these two equations
2d - s = 28
-d + s = -5
---------------addition eliminates s, find d
d = 23 is the daughters age
:
Find s using the equation -d + s = -5
-23 + s = -5
s = -5 + 23
s = 18 is the son's age
:
Use m = 3d - 24 to find the man's
m = 3(23) - 24
m = 69 - 24
m = 45 is the man's age
:
Check this in the equation: m = s + d + 4
45 = 18 + 23 + 4
45 = 45
:
:
 how old is each now? man is 45, daughter is 23, son is 18