Question 158770: In 5 years, Dad will be three times as old as his daughter Jill will be then. If the sum of their present ages is 50, how old are they now?
If x + 5 is Jill's age five years from now, which of the following equations could be used to solve the problem?
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! i'm not sure what equations you are looking at, but the following equation will solve the problem.
let D = dad's age now.
let J = jill's age now.
D+5 = dad's age 5 years from now.
J+5 = jill's age 5 years from now.
problem states that the sum of their ages now is 50, so
D+J=50
problem states that in 5 years dad will be 3 times as old as jill will be then, so
(D+5) = 3 * (J+5)
to solve this problem, we remove one of the unknowns by expressing it in terms of the other unknown in one of the equations.
i took D+J=50 because it was simpler. i could have used the other equation as well. either way it will work.
if D+J=50, then D=(50-J)
taking that relationship and substituting for D in the other equation, it becomes
50 - J + 5 = 3 * (J + 5)
this becomes
50 - J + 5 = (3 * J) + (3 * 5)
this becomes
55 - J = (3 * J) + 15
this becomes
55 - 15 = (3 * J) + J
which becomes
40 = 4*J
which becomes
10 = J which is the same as J = 10.
if J = 10, then D = 50 - J becomes D = 50 - 10 becomes D = 40
so jill is 10 years old today and dad is 40 years old today.
5 years from now, jill will be 15 years old and dad will be 45 years old.
45 is 3 * 15 so the requirements of the equation is satisfied.
if you substitute y for D and x for J, then these equations become...
(x+y) = 50
(y+5) = 3*(x+5)
y is dad's age now.
x is jill's age now.
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